That was exactly what I was looking for. I'll see if I can get an SPL, there is probably one around here at work. ...
So the signal-to-noise dB ratio won't do me a whole lot of good, because I have no "known quiet amp" standard against which to compare. But it's an idea for you.
The input jack question wasn't directly answered (or I misunderstood)... Are the input jacks new or reused? Have you verified good contact for all the shorting switches on the input jacks? If they were working correctly, I'd expect them to be shorting the input stage grids to ground with nothing plugged in, leaving only the little bit of resistance of the paralleled 68kΩ resistors.
... Does anybody know of a link that shows how to make nice cable that look more vintage? I have to get rid of these as well because of how far they stick out the back.
I don't know if the old crappy RCA connectors on the vintage Fenders are even still sold. I can tell you they are a huge pain to work with for making your own cable (I've done it, but it's been about 20 years).
... What can be done about the hum in the reverb? ...
If you're going to tackle that, you need to divide & conquer.
Pull the input tube out for both channels; you don't want any noise from before the reverb complicating your assessment of the noise level. Yank the 12AT7 reverb driver tube. Unplug both cables running to the reverb pan from the jacks on the amp. Work on getting just the reverb return stage, the mix gain stage, phase inverter & everything after quiet.
If/once that part is quiet, add the tank back in but not the driver tube. Rinse & repeat until you have everything back in the amp.
There's no sense in me guessing what might be the noise source blindly, unless you've gone and narrowed it to a particular segment of the reverb circuit. The cables & pan may be fine... I used a crap pair of RCA cables that came in the box of a $40 CD player to hook up reverb pans, which ran acceptably-quiet for years. So the best course is to verify rather than have "expert guesses".