Wow, what a cool cruiser! That thing should absolutely be preserved. Its in way better condition than the 1978 Freeborn Red Im trying to save!
Id read that thread mentioned above. It may be mentioned in there, but another thing Ive heard that you should do in this situation is to kind of condition the paint before you start putting any sort of rubbing compound to it. Basically Id start by pressure washing it, but not too strong, then just hand washing it with some good car wash containing carnauba wax. Hand wash a few times. Then from there just start compounding it. Im just using basic Turtle Wax rubbing compound for heavy oxidation, doing it by hand one section at a time, and its working well on my original sunburnt and stained Freeborn Red.
Whatever you do, dont let anyone talk you into painting it!