I was in the OP exact possition. Also, I'm from Houston as well. I got taken through the washer on my trade, and my payments went up $100, but t's worth it. So worth it. Just make sure it's the exact car you want.
Your strategy should be like this:
First, on a 2012 GT, accept no less than Invoice minus dealer holdback minus all rebates. That should knock off 7-8K off the sticker.
Second, try and line up financing before you get to the dealer. Don't mention this until after the deal is done. Trust me, if they give you a good price, they can always screw you on the financing.
Third, don't accept their first offer on your trade. They're just trying to low-ball you.
Fourth, don't be afraid to walk away. They're are plenty of dealerships in Houston willing to do the deal exactly like I outlines above.
Fifth, I would strongly recommend checking out the inventory at Southern Ford off 288. They give a lifetime warranty on all cars. That's worth 2K+, so that should help ease the burden of your trade loss.
Sixth, enjoy the hell out of your GT, but don't get stupid with your speeding. These things get into the 100's so easily.
Seventh, like a previous poster said, consider the savings on sales tax when analyzing your potential net loss.