maintain GA mode longer if possible
altaflyer,
The operation I am with has us acelerate at 1,000, except at special locations. At 1,000 in the GA mode, you can select a higher speed and the jet will acelerate and you can clean up to flaps 5 (or whatever your plan requires) all with 3 autopilots in control. As long as you do not have to change your GA course, you can keep 3 autopilots in control. As others have already stated, the moment you select HDG SEL or FLCH, or any of the other options, you revert back to the original autopilot, and you have the rudder at the point.
If you did a missed app (vs. the go around stated in your question), I would assume it would have been due to weather, which would have probably required APP (and 3 autopilots) selected.