The fliht plan, between KSEA and KSFF, that loads with the 707 is needed so that the Doppler navigation will work properly. Because it loads with the 707, it overrides the flight plan you save the flight with.

Just reload you flight plan, do not move to the original starting airport, AND if you ysed the airport you stopped at as a part of the route, FSX, and more importantly, the GPS, will set the route to continue from the airport you are stopped at.

For exmple. I created a route from YPAD (Adelade) to YBBN (Brisbane), via YMML (Melbourne) and YSSY (Sydney) -I know these are very short legs, but it was a test - and when I reloaded the 707 at YMML, then reloaded the route, the GPS was showing that the flight would do the YMML to YSSY segment of the route next.
Note. I used the Airports ID's themselves as waypoints, and there was no data for the route from the start aiport YPAD, to the first destination aiport (YMML), due to the KSEA to KSFF route being reloaded with the 707 for the Doppler navigation to work.

I hope this all makes sense for you, and helps you to do understand how multiple stopovers for a flight for the 707 Captain work. ;)