I have to say that carpentry is my favourite of all the trades that I work in. The obvious route is of course a trade apprenticeship, but these aren't always easy to find.
I never did one though. I simply drifted into labouring for a small local builder. You may not want that spread of trades. In your case, you might go for a local carpentry specialist. You may have to ask several before you find one that needs a helping hand. In time, experienced gained can easily equal the formal apprenticeship route.
If you can afford the fees, an introductory course at your nearest college or training centre would certainly put you in a good position to have something to offer a tradesman.
Physically, it need not be too demanding. Sitework would give you no problems. Benchwork may take a little getting used to with your height and back problem though. I'm 6ft, and I can find that stooping over a bench for long periods can be tiring. All in all, it's a minor point. There's always a way around everything.
For wages ... not a lot when you start of course. Subcontract sitework can earn you a lot, but you have to be fast these days. If you can progress to being self-employed eventually, there's a very good wage to be made from building up a list of happy customers. That's especially true working on older, period property. The kind of specialist thing that the subcontract "fliers" just don't want to do......... because you have to think"
Very best of luck if you do find a way to go ahead.