That tank looks a lot like a couple that I had several years ago. I used the standard aluminum-safe paint remover, I guess that's methylene chloride, and it worked fine. I was living in TX at the time, and of course it was legal there. Turns out it's pretty nasty stuff, and is now banned in several countries. I like the heat gun idea. The other thing about the paint stripper is that it did attack the galvanizing under the coating, just more slowly. If you can get it off without disturbing that galvanizing, all the better.
Those PST LP72s were my favorite single tanks for local shallow diving. When I moved I sold all my tanks except 2 AL80s for working on regulators and the (very) occasional local SM dive. I'm sure you'll get lots of use out of it!