The only disadvantage I can see from trading AFTER the cut to 27 would be those trades that exchange an unequal number of players (2 for 1, 3 for 1 etc.). That would mean that teams could end up with less than 35 players on their roster after the FA draft, which really shouldn't be a problem. Otherwise, I agree with the trade period being after the cut to 27 and the CAP enforced.
I also like the FA draft random and in reverse order after each round. For me, it adds to the anticipation and gives EVERYONE the same opportunity to get a low first round pick.