Hi Xavier,
It's quite perturbating to move from a navigating system to another, and this is what ⌘T provides, for someone used to the drawer.
My proposal is: a project drawer embedded in a separate window/panel.
From what I understand, the drawer is going to be seeing an overhaul on TextMate 2.0 (ETA is sometime *after* the Leopard release).
Until then, you've got to work with what you have.
If you want my opinion, though, I'd suggest to just not use TextMate in some hacked Full Screen mode ... "Full Screen"-edness is something that's waaaayyy too overrated, anyway ;-)
-steve