Today's Mystery Guest (RCA CTC-4)

[dtvmcdonald]

Does it work with the capacitor from the
previous stage and the two outputs of T115 disconnected?

I would suggest the next step after checking that is to use the new transformer plus a complete set of new parts, including tube and tube socket,
and build a breadboard of the whole thing leaving out the capacitor
that connects to the previous stage and leaving the two outputs of
T115 disconnected. Run it off any 250-300 v power supply.
There is no need for short leads in this circuit, leave them long.

You need to get that working and then transfer parts to the
main chassis. These oscillators can be picky.