I have a 91 Reatta convertible. When I took it out of the garage, it lost rear brakes. I found the rear brake line in front of the left rear wheel rusted through. A quick check found rust on most of the other brake lines. I intend on changing all the lines to Stainless Steel. My question is, with all the problems with the anti-lock brake systems in Reattas, has anyone tried to eliminate the anti-locks and re-plumb to a standard system? Is this even possible?

The 1991 has what is considered current technology. You have the standard master cylinder and ABS brake system. In my opinion there is no need to look to make changes to your cars braking system.
What other posters have been talking about is retrofitting their Reattas[88-90] away from the Teves braking system.

Stainless steel lines will be very expensive and very unnecessary. Spend the money on a high quality bender and bubble flaring tool. Keep the fluid fresh and you will have fewer problems down the road. The lines on your 91 are 17 years old. Replacement lines should last at least 10 years. Your fuel lines are most likely just as rusty. That spot in front of the left rear is notorious for rust issues.

The section between the rear wheels can be replaced with a $5 60" piece from Advance Auto without splicing or flaring. It won't be in the exact same place in order to reach, which is okay because the original location SUCKS! Steak