It is always better to go around and take your time to set up the approach.

What is wrong with the little black button on the yoke? Disconnect the autopilot, fly the plane to where you want it - smoothly, then re-connect the autopilot and continue the approach as long as you are out far enough to do it safely and not rush.

The computer needs a bit of time to track the LOC and G/S so it can compute the wind etc. Remember in an auto land, the 3 FCC's need to talk to each other and agree, so as to complete the full 3 autopilot landing - all that takes a bit of time. Also, the tracking is important so the computers figure the drift for the input to the rudder. A lot goes on when the other two autopilots are engaged.

A good landing begins with a stable approach.

Lou