I like Model Ts because lots of people have considered them to be out of style and uncool. All the more reason to build one, if you ask me. Just don't chop it. To me, Model Ts look best with the tall roofs.
The early Shay cars had correct rumble grab handles, cowl lamps, and taillamps with all red lenses. We at Specialized in Houston, among others, sold them luggage racks by the hundreds and other parts. Later models like yours have the funky handles and lamps to rduce costs. Specialized sold many Ford script upgrade parts to Shay owners including bumper clamps, radiator emblems, hubcaps, runningboard step plates.
Here's a couple pics of the T when it was in Grandpa's dirt floor garage circa 1990. Grandpa was a bit of a hoarder too. And the Shay being loaded this week going off to a new home in Arizona. It only had 7,332 miles on it - only took fresh fluids, a battery and new fuel pump to wake it from it's slumber. Even with fogging oil in the cylinders, did not smoke at all. Going to be a good little runner for the new owner.
If it's only worth $2K then I'll give you that for it and I'm sure hundreds here would. Come on a fiberglass body costs more than that. It's titled so is the perfect base for a wicked hot rod. You could part it out for more and still have the body and title for a rod. Maybe Model-As will go that way soon! 32-34s will never follow though.