Hello tempus, are you still with us? Don't forget to pull the plug, eh!
I suggest you search for a brand and model #, then search at
rec.antiques.radio+phono, where there are expert advisors on how these
units can be fixed. The transformer you saw was for the output to the
speaker. You are dealing with a live chassis unit. the "death cap" may
be shorted, and the hum you here is 120vac running thru the chassis.
The filter caps may not be too bad, although they are always leaky at
that age. You can use 50-80 uF for the first 2, then drop to 20-30 for
the other 2. There is no diode tube to worry about. If the diode is a
bunch of square plates with a central bolt, it is selenium. Replace it
with a new silicon diode and a resistor. Cheers.

John Kogel