Have a shower faucet (American Standard) in house built in 1966. Hot and cold water do not mix properly. Trying to find parts or replacement as a new fixture would require replumbing the pipes. Any ideas?

If you shop around you should find replacement parts. Faucet Part - Bathroom Product List - Faucet Parts I'd explore that and stop by a good plumbing supply shop long before considering replacing the entire mixer. Take your cartridge or ball valve to the shop and shop it to the guy at the counter. You'd me amazed how many times these guys reach on the shelf and hand you a new one.

Try the company.

Last year, I had several vey helpful people at American Standard identify and supply replacement parts for a 1995 valve.