Hey MiniDoctor
Sounds like you want the best of both worlds, which we'd all love but really isn't practical. If you want this car to go on for years, be sound and look like a lovely classic, something you're proud to drive then you need to spend the money, preferably with an experienced reputable company who knows minis inside and out... this ultimately will give you the result you want.
The upfront cost that any repair company gives you will be a bit confronting, but break down it - for example if you plan on having this car for the next 10 years then think well I'd only be spending "X" on it a year, which for a classic car that has been expertly restored- in reality it's pretty fair, and seriously a good investment because a 1966 Mini in good condition in 10 years time will be worth some real money... If you can bear to part with it that is

Good luck fellow mini lover!