I would start with just the caps in the power supply.
If your amp has the original Astron tone caps keep those if at all possible. These are now fetching a lot of $$$$ at times and are hard to replace.
The power supply caps (under the cover) are usually all that need replacement.
The hiss is probably V1 and/or V2 that may be a bit tired (if original) and need to be cranked higher than necessary to get a given level. Maybe pull these for a minute and stick some generic fresh new 12AX7s in there and see if this does the trick. If it does, then find some good 12AX7s you like. Actually, try a spot check of each socket with a new tube one at a time.
Clean and lube the pots with real tuner/cleaner/lube stuff not something like WD-40 or just cleaner.
If you are close to L.A. I would be happy to do this for you at n/c and bias the puppy. I have a soft spot for Fender BF era amps. Myles, you're a gem!
Actually, I'm on "the other coast" so I can't take you up on your generous offer, but thanks for your great suggestions. I'll be all about it as soon as I can get the power supply caps.