First I'll say you are very patient. I feel bad for anyone who has these problems that don't get fixed. What are the odds of three regs being bad?

The high side of the reg should not bleed off into the low side. I might expect it from an old used reg but not a new one. Since you purged the tank valve before installing the reg I would think that no foriegn objects were pushed into the reg itself. Only disassembly would tell though. I wish I had a way to fix it for you.

Do you know of anyone local with a welder that you could borrow their reg?