In theory, Manpower Planning can relax the restriction at their discretion so it never hurts to bid the 737 if that's what you desire. There have been a few recent cases of probationary pilots switching between the 737/320 despite the training freeze. You can be awarded the 76T as soon as you can hold it in a bid. Note that your A320 freeze would disappear and you would have a new two-year 757/767 training freeze. This would limit you to switching between the 76T and 756 (via a BAT) or bidding the 777 or 747 until the freeze is up.

BUT....with an Oct 7 class date it's entirely possible that the only thing holding you back will be IT if you are not fully in the system prior to the bid closing.