You can go mid 11's on a TE44 with a fairly stock setup. The key is getting a good launch and running at least 22-23lbs boost on stock heads. You didn't mention anything about your suspension setup or anything, but you should be getting 1.6 60fts or better.
I put a TE44 on my white t last year for a couple months and ran 11.6s right off the bat with a 1.60 60 ft at only 113mph on alky. The setup was fairly stock except for good exhaust (THDP and ATR with cutout), good trans (Dynotech Hi-Pro), and good suspension parts and tires (H&R rear sway bar and 28" Mickey drag radials). Also used a stock intercooler with a dutt neck and a stock MAF, so there was probably some more gains that could have been had.
I use Directscan along with EGT for tuning along with a turbotweak chip. Various launch techniques tried off the footbrake until I found out what my car likes. Seems like you have a lot of parts to start with, but the little things become more important. Make sure the cooling system is working well, watch the boost to make sure its steady and not creeping, shifts are tight, etc, etc. Also, you didn't mention the converter or locking it up. A restalled stock converter or a slightly better one might help if the current one isn't enough. Locking usually helps on a stock setup too. Weak valve springs will also hurt performance. Like I said, lots of things can hurt performance if they aren't up to par. Good luck!