Hmm, I really don't think I'm going to attempt a step by step as I'm sure I'd confuse things even further.
But, I would say that in general a 20' downclimb shouldn't be that hard. The bounce would certainly complicate things, but for me, in general a 20' downclimb doesn't take much longer than changing over and descending. I'd suggest that in addition to solving the change over problem, working on this might be useful in those limited edge cases.
Also, I don't use a "QAS". My frog is simply a croll and right-handed petzl ascender (another "no-no" some will tell you
Ok. I guess I will try to describe what I do. (going on memory here.. too lazy to get out my frog and try it right this second.)
1) put upper ascender at about 80% of my normal maximum (guessing on the distance here)
2) Sit on croll
3) weave rope into micro-rack (which for me is directly attached to my D-mallion, another "no-no"
and do a hard lock-off.
Do this beneath my croll (since obviously no slack above it.)
4) Stand up in foot loop and as I do, pull on release on croll
5) pop rope out of croll
This should put my weight fully on my rack at this point.
6) lower the upper ascender to just above my rack (don't always do this, but generally do)
7) Unlock my rack, let it slide an inch or so... do a soft-lock off.
8) thumb upper ascender off the rope.
9) undo soft lock and descend.
If I'm focused I can do the above in under 20 seconds. BUT that wasn't on 140' of rope where bounce will have some impact on all the steps.
If you have a long rack, then well.. I can't help you. I'm WAY out of practice on that. (hmm, I probably should swap racks and practice a bit.)
I should note too that I have what some refer to as a 3 cowstail system (ascender on its own tether and then a Petzl Energia for my "normal" two tethers.
As for feeling like an idiot... No, an idiot would have had the problems you did and not asked for help. Everyone (ok, maybe 1 or 2 folks) can always learn and improve their technique.