After some investigation, the autopilot is a Trutrak "Digiflight II VSVG" and it is in GPSS mode. The GPS is hooked up with an ARINC converter, so it gets all the necessary data.
So, I think the hardware is suitable, and I think I just need to be more precise in getting to the proper altitudes on each approach segment (unless getting steered in with ATC vectors).
Thanks Bob and Alan for responding. Much appreciated.
Jim Schwartz
RV-10 N921AC