Your suspicions are correct and you are well on the
way to a new tranny - stop using the amp immediately.
Now, being a vintage amp, I'd recommend that you
take it to a competent technicial familiar with tube gear.

If you decide to do a bit of initial diagnosis here's a
QAD ("quick and dirty") diagnosis - from being "dead"
cold, off for 8 hours or so, pull the rectifier tube
(should be either a 5Y3, 5U4 or 5AR4/GZ34 depending
on the model, probably the first) then turn the amp on
with your hand on the power tranny. If it starts to get
warm, take it into the shop! If it doesn't, replace the
rectifier and pull the two output tubes - should be 6V6s
but there was an odd model with 6BQ5s. Turn it on
again and see if it gets hot. If so, then it's DC power
supply problems, if not it's probably in the output stage.
For the first changing the rectifier may help but you
probably need a cap job. For the second you can try
replacing the output tubes.

No matter what you find, unless you're somewhat
experienced, I'd take it to a tech - just don't want to
lose the original tranny.