If you love doing handwork, I'd suggest using a stripper (3M Safer Strip and Citrastrip Orange are less toxic, but slower) and steelwool, wear gloves, do it outside on a thick layer of newspaper. If you want it done fast and painless take it to a blaster who uses a glass bead media (or something similar that's not super-aggressive).
The new shots make me more than ever convinced it's a British builder, it shows some nice touches like the Wagner forkcrown and good tube mitering in the BB shell. The forkblades look especially nicely curved, seatstays look like single-tapers, and combined with the geometry, these are things that makes me think it might be built later than early '70s...even tho all those other clues: the little RD cable braze-on, the nutted brake fittings, lack of any other cable guides, etc. all point to an early '70s date. Looks like it was originally red, over white (?) primer...nice (mystery) bike!