my only concern is this...your 20g qt tank now contains fish that have ich. i know you said this qt is cycled. however (and hopefully steve can chime in here), unless you empty/sterilize everything in your qt, you will be putting fish back into the same water that they were in when they had the parasite.
while ich needs a fish host to live, there is still the possibility of the parasite living in your qt during the time you are doing ttm. i would think you would want to start fresh with a sterile qt. obviously, you won't have time to cycle it once ttm is complete and it's time to put the fish into qt for the remainder of your fallow period.
i have never used a cycled qt. i simply set up my qt when i was getting a new fish. i used prime as a precaution but also did simple 3-4g water changes every couple of days (qt was as 10g). i never had a problem with ammonia. you should also have an ammonia alert badge on your qt.