Tried the "clean the tube pins and sockets" idea.
Removed each tube, ran 800 grit sandpaper over the pins. Used a rat tail file to clean up the socket holes.
Sudden volume increase problem has apparently disappeared.
Still need to eliminate the 60 cycle hum - but the A-K sure sounds better now.
(Also found a Heathkit TC-3 tube tester for sale!)
if you have 60hz hum, it is a sign that the capacitors are leaky.
I would start by inspecting resistors to see if any of them are cracked- if they are in the voltage control, a resistor opening could increase voltage significantly. Likewise leaky caps will change value as they heat. A cap shorting out in the tuning could significantly increase voltage to the amplifier stage.
In any case... to prevent destroying the tubes / power transformer (I assume it has a transformer and isn't like a AA5 which puts the tubes in series) you need to start with capacitors. Leaky caps (electrolytics) will significantly increase current flow on the transformer and overheat it. You want to look for the round caps, which if they are old likely will have wax leaking out of them - other caps (mica etc) most likely are just and since they may be very accurate / chosen values don't mess with them since it will likely affect the radios performance. Electrolytics can be replaced with modern "close enough" values with no problem.
to run the radio for diagnosis, you can (should) put it on a "dim bulb" this is just an incandescent bulb wired in series in the power lead. Properly working, it should start fairly bright ( cold filaments) then start diming as the filaments heat and finally get a bit brighter as the tube current starts. You need to experiment with different values of bulbs.... since they will change voltage to the radio
Next inspect resistors for any signs of cracking. when you have the chassis out of the radio and turned on, take a chopstick and gently tap on resistors one at a time.. if they are cracked you should suddenly hear noise, or the increase in volume. just KEEP YOUR HANDS OUT you don't want to experience the high voltage!!! Taping can help find loose connections.. If you have a dim bulb, you may even see a change in brightness if you tap a problem location.
Here is the little Fender I built a few years ago