Howdy from NC - 71 Demon
Welcome from another North Carolinian. Like the Demon and the fact that it is a factory stick/V8 makes it fairly rare and very cool in my mind. I like your plans for it and your memories and the family connection make it really valuable to you, and that is what counts. I think your tire size should work on the rear with wheels and backspacing. Others can chime in on that.
BTW, even though I am a 4spd guy, I wouldn't rush to replace the three speed, unless you want a 4 spd really badly. I think it is another "cool" factory for your particular car. Good luck on the build and keep us posted.