Okay. After several more days of digging and experimentation I finally found the answer to my own question. To get the (next) subtitle image I used:
// access the subtitle track
Track theTrack = [self getVideoSubtitleTrack];
// set flags to find NEXT image (ignoring the current one)...
myFlags = nextTimeStep;
// ... and search forward from current position.
GetTrackNextInterestingTime(theTrack, myFlags, playheadPos, fixed1, &nextInterestingTime, NULL);
This only finds the start of an image object though, and iterating through the track finds the leading edge of each successive image. But I wanted the end time of the current text too.
After getting the start time, I experimented with the seven available flags and found that setting the flag to 'nextTimeTrackEdit' gets the end time.