Tires explode way under rated pressure limit
You say that you have a large gash in the inner tube. And you say that the tire was thrown off the rim. I assume that the thrown off tire was the cause, not the result of the explosion.

The point is that it's only the tire that is expected to counteract the force of the pressurized air, not the inner tube. The inner tube is for sealing only. Thus, when the bead of the tire jumps out of the rim, this will instantly kill the inner tube: it's simply not designed to withstand the resulting forces. So, the question is: How can the tire jump out of the rim?

You say that you are refurbishing an old 70s bike. Afaik, there have been different ways that tires attach to the rim. I think I recall reading something about rims which were flat on the insides of their sides. Such rims would require tires with very strong beads. There also was a system where the bead was somehow clamped into the rim.

Thus, I would suggest to check the form of the rim. I may be wrong, but if you don't find a small bulge on the inside of the rims edges that holds the bead in place, that's most likely your problem.