Welcome to the world of old tube equipment. :/
That popping sound is usually the sound of boiling tar in the transformer (and
of course the latent heat keeps it boiling after power is turned off). The
symptoms you describe are not unusual and it's most likely a short in the
transformer.
If, as you say, only some of the tube filaments were dark, it may be that
there are multiple filament windings and one of them developed a short.
In equipment of that sort, shorted caps don't usually present such a degree of
problem to the transformer. The vacuum-tube rectifiers have some
hundreds-of-ohms of plate resistance, as well as maximum emission (current)
limits, and act as a limiting impedance for shorted/leaky caps.
If it's any consolation, there probably wasn't anything you could do to avoid
the failure.
I pulled out the schematic for a Stark OSK-4, a very basic vacuum-tube 'scope,
probably similar in category to the DuMont. Here are some observations which
may (or may not) be of assistance in your situation, if you are RE'ing the
power supply:
- The CRT accelerating potential does not come from a high positive supply
for the anode, rather it is a high negative supply for the cathode. It is
obtained through a half-wave rectifier, supplied by a transformer winding
internally stacked on one side of the main B+ winding. The filament for the
half-wave rectifier is obtained from an additional tap on the high-voltage winding.
- The CRT has it's own filament winding, as the cathode is operating at a
high potential and the cathode-filament insulation potential is limited. (In
other words, the transformer is providing the high-potential insulation.)
- The B- (center-tap) does not go directly to ground, rather it goes through
some resistance to ground so as to develop a negative supply (for cathodes of
the V input amp.)
If there's no rush and you're willing to wait on a possibility I can poke
around the radio museum here in the next couple of weeks to see if there's a
junkered/junkable DuMont (let me know the model number). We have piles of old
vac-tube scopes that we should get rid of and I know I've seen a DuMont or
two. Shipping (cost) would be from Vancouver.