If you Google you will find the Stec ST 901 Manual. This is the info page for the T approach you described. From your description it seems that the issue you are experiencing is that the S-Tec is not intercepting the various segments in a timely manner. I think you believe that it needs to have a greater bank angle to resolve the issue. However typically the IAF’s are not fly over points. Therefore the unit should calculate and turn prior to reaching the IAF so that it smoothly ends on the next segment. If this is not occurring and you are using the unit in accordance with the manual I’d suspect it needs adjustment. Best course of action is to take it to an Stec dealer who regularly works on this autopilot. It could be a simple cable adjustment or reracking the control head etc. The servo might also be drawing high starting voltage which would slow its startup and cause it to fly thru the course. These autopilots are relatively bullet proof so should not be that costly to diagnose and repair.
3-6 5th Ed. Feb 15, 08
S–TEC
Fig. 3-2. GPS-T Approach
1. a. Set the Heading Bug under the Lubber Line.
b. Engage the GPSS Converter's HDG mode.
c. Engage the autopilot's HDG mode.
d. Program the GPS Navigator with the desired approach.
e. Engage the GPSS Converter's GPSS mode.
f. The autopilot begins tracking to the Initial Approach Fix (IAF).
2. a. The autopilot intercepts the IAF, then makes a 90° turn, and begins tracking to the Final Approach Fix (FAF).
3. a. The autopilot becomes established on the inbound course.
b. At the Missed Approach Point (MAP), disconnect the autopilot for a landing or go-around, as required.