Kurt, it seems that you stand at the virtual restoration crossroads: undertake a complete tear-down, or, maybe take an easier, faster, less expensive route and just enjoy the car?
This is a tough question and involves your personal finances. It's easy for me to say "body off, do it right", but it ain't my money and time! However, since you asked, I say <span style="text-decoration: underline">do it right</span>: take the body off and replace all bad parts. Document everything carefully with photos so if and when you sell the car, the next owner will have his provenance (and you'll be able to fetch top-dollars for the car!).
Please post photos of your restoration on this rare and beautiful Triumph. There can't be many nice ones left, I think your rebuild can be a significant contribution to the Triumph marque.
Good luck, please keep us posted! :thumbsup: