Much of this might be very rudimentary, and I certainly don't mean to insult your intelligence with any of these, but I'll take a few stabs at it.
Is the whisper key getting down fast enough? Is the whisper key sealing completely? With any half hole notes we have to make sure the whisper key is down or there could be instability issues (although usually the problem is tone or intonation).
Are there any leaks in the A, B or C keys? Same issue as whisper key, we don't want leaks.
If any finger is late in coming down I would suspect the middle finger of the left hand. Especially since that one is on a somewhat awkward tone hole, both in it's placement and it's slanted direction, it's easy to let that one leak.
Is there debris in the F tone hole under the first finger? Or debris in the tenor joint? Pipe cleaner the tone hole and swab out really good. A bit of debris (or spit for that matter) could make unpredictable results in half holed notes.
I agree that 1/4 hole is probably more accurate than 1/2 hole for Ab/G#. I know many players that leak way too much.
Anything you can do with the reed? I know if my reeds are closing up on me they'll produce this kind of negative behavior. Maybe try opening the tip from the first wire just the tiniest bit to add some resistance (if that's really what's happening) to that register.
Ab/G# is a crummy note. We all have problems with it sometimes.
I hope some of this was helpful, although I'm much less experienced than other members of the board, these are the things that I would check for.
M.M.A., D.M.A. University of Illinois at Urbana/Champaign: B.Mus. Lawrence University
Bassoon professor at University of Wisconsin Eau-Claire
Maker of the Little-Jake electric bassoon pickup and Weasel bassoon reeds