I couldn't find the one I wanted in the list (#1-#9)
At which list are you referring to, Mark (famous driver of the M-RKOZ 707)?
That flight plan converter tool gives you a list, but these items are just nice to have, not mandatory. I think that it only offers the enroute ones (you overfly them), no stations with an offset to your route.
You can use and enter every DME you can tune. It only takes the coordinates there, so maybe that's the point where you are currently struggling.
It would need some charts or flight planning tools to see them. I'm using payware but maybe some freeware or even the map in FSX (haven't tried it) shows you those coordinates.

See an example here of a neat payware tool from Aivlasoft.

So you would enter the DME update mode, enter the coordinates of the corresponding DME (after tuning it) and use its position and readings to update. 4 (DME) stations around PHNL there.

My last flight in the 727 (twin Civa INS setup), where I used one offset and one enroute DME, even gave me a "0" on the accuracy, leaving me surprised since this is the highest rank possible there. As said, one overfly and one offset DME was used and I've changed the stations when getting more than 100nm away, so no extremely high workload there when in cruise.
But the trip was only 600nm long, so maybe that has to be considered too.

Am I the only one wondering to which statement he's referring to with "oh yes"? 
You have a somehow sad forum name, Sir. 

Mark, I have a few questions towards some expressions used as I don't fully understand them.

Once I come into range of NGF a few minutes before MKK (followed by CHK a few minutes later), I start the alignment process, making sure not to initiate it until CHK has come into range (I'm not sure if that helps or not with it being part of the flight plan).
So do you start alignment there or not?
If the thing you have tuned shows a DME value and you're aware of the coordinates, just start it. There's no other dependency which has to be considered then.

That ID number being displayed corresponds to the available "presets" inside the CDU. The are available from 1-9 and can be loaded via that ADC file the plan converter creates.
In the creating process, you can mark "ADC" on some waypoints and those waypoints will appear in the ADC file then.
If you load that ADC file into the Civa (via the ADEU reader, just like you would load a flight plan, which is AWC), the coordinates from those selected waypoints are written into the preset storage.
So you just have to check their coordinates later, instead of having to enter each one manually.

You can also add waypoints to this preset list which are not part of the flight plan (all offset waypoints=stations would be handled like this).

The thinking behind this is to reduce workload and enable some planning in the question of when and where to update the CDU's position.
So these ADC files contain all your planned update stations and their coordinates with being selectable by this very ID you spoke of.

Here's an example plan from Melbourne to Brisbane.

It gave me two AWC files (the actual plan to follow, including all the waypoints which actually get overflown by our plane), YMML to YBBN.1AWC and 2AWC. The contents of these files can be seen on the left side.

On the right side, all waypoints are shown and also their type is described. As we can only update on some VORs (DMEs to be precise), all those "Intersection" waypoints aren't of any use here.
As you see, the VORs are already marked with "ADC" but two of them are unchecked by "In plan", so they don't appear in the left side view and therefore won't be overflown by us.
What's their use?
Note: You have to manually get them out of the plan (=uncheck "In plan"), otherwise the Civa will try to overfly them.

Look at the view in the flight planner, to catch their location.

See them, namely DU and LAV? Those are the "spikes" on our plan. We don't want to fly that spiky, do we?
As they don't get overflown, those will be some VORs with an offset to our route. They are only included in the ADC file, not in the AWC (left side view, which defines the actual flight plan).
Lets look into this ADC file now and see.
Quote:

Four VORs are named there and each of them has an ID now. This is the preset which can be used later.
So if you want to update on one of those four, make sure to load the ADC into the Civa (don't worry, it won't harm your flight plan there, it just writes into the preset memory) and later look up the corresponding ID of the "update station" to use. That's the point where CDU Keyboard Push DME ID Number enters the game.

As said, this setup requires some planning first and enables some comfortable way of updating later.
I must admit, I rarely use it, if ever. I just watch my charts, look up some DME, tune it and enter its coordinates by hand, so I get rid of this planning phase and just feed the Civa with my flight plan ADEU cards, not the ADC ones.


Your way of using the FSX map for planning is clever, Mark. Although not as comfortable and effective as some payware around, it comes for free and is already there.
So you are, once again, showing that you are a clever user of resources.

So, what holds you back on starting the DME update then?

A common situation would be that you see some nice DME coming into range. You may also see that your CDU could need some update.

Steps are
1) tuning that station
2) switching the CDU to DME update mode
3) entering the coordinates of the tuned station
4) checking, if the rough distance (shown on the CDU display) matches the DME measured one
5) starting the update

Takes some seconds, so even 500 kts GS (I sometimes go 1100 there  ) can't hold you back there since the measurements (CDU value and DME display) are updated in realtime.
If you use that list feature I've described, you even get faster because you don't have to enter the coordinates as they are already pre-set.
I'd like to help you with that "aha" moment, Mark, but, currently, I can't see why it's not happening.  

I think that on the real thing, you would get quite some offset then. You can't measure this offset (since you haven't any reference there), that's why you would want to avoid it.  

Now, in our Sim, the thing loses its navigational accuracy when going above "5" on the index. So your "9" is the max offset it can show (meaning your are "unlimitedly" inaccurate) and well beyond any limits for using it as navigational source.
Now, as said before somewhere, I don't know how FSX models this wrong nav source then. It could well be that, in the Sim, your ac stays on Course even if the INS doesn't really know where you are.
We just have to be aware that this isn't the way the thing should be operated and, also from my viewpoint, not of any fun to let it just go down the drain.  

So far, I only ran into trouble with the updating when over the Atlantic. My index went above "5" there and I was glad to see the first land based Nav sources coming into range. So I could bring the index down to below "5" within some minutes and was well aligned when reaching the landmass.
I think that the real planes don't lose accuracy that fast when just flying some "straight" line over the Ocean, that's the only explanation I have for them since they needed to be fairly accurately placed on this NAT track system, to avoid separation issues there.
The "needed" comes from the fact that most planes (if not all) on those tracks nowadays use their GPS which offers far more better readings and also maintains itself when compared to the old INS.

But my main question still remains. What's preventing you guys from updating the INS when some DME actually IS in range?
Something unclear on the procedure?
I can only recommend an installation with those green nav flags showing. Easy to see if you failed on entering the data there, no more questioning "will it update now?". The CDU shows some indicators too, but they are far more subtle than those green flags.
Since my first Civa operations often ended in the thinking that I am updating but in the fact that I did not, this looks like a big help.

Flying above some landmass will always give you enough stations to perform an update. The only places I remember for having only a sparse placement of stations (to perform an DME update on) would be eastern Russia or something. I had tons of NDBs there but only few VOR DMEs.
Being at high altitudes, the DMEs often radiate across quite some range though, so you should be ok in cruise while on the descent, the local nav sources (and not the INS) come into play.

From reading your steps, I can't see any item which should prevent the update. So I'm puzzled. 

At least, Mark, reading from your experience was fun. 

I'd really like to help you there, but I don't have a clue where to start. That turning away motion could arise when you were too late on changing the ADEU cards.
Civa then reads the next waypoint (which is one that's already been used) and tries to turn to it, so the backward direction will become active, I think.

Before this happens (running out of current waypoints), those ALERT signs will start to blink (not only light up, as they do when getting close to a new waypoint) though.
I've had this on stages where you should change the ADEU card when going from 6 to 7 on the list and the distance there was like 2nm or so.
Or I forgot to watch my Civa and only wondered why the plane takes such a strange direction. Luckily, when you realize this thing happening, the HDG mode can be used, the Civas get a new ADEU card and you then can look up the next waypoint on the Civa's list.
In the meantime, you can correct the heading roughly via the bug or, when you were to late on realizing, fly a circle and continue like nothing has happened.
Maybe say something like "oh, dear passengers, did you see that small house on the left side? So cute!".

Always have that small text file open which is compiled by the flight plan converter. It shows you all distances (so you can prepare for such short ADEU interchange times) and also lets you plan ahead.

The last part in assuming your position always is to listen closely to the ATC's accent.  
This even works when only flying online. Those NZ guys just sound different.