Today's Mystery Guest (RCA CTC-4)

[old_coot88]

I'd say the tube socket is fine, provided there's no intermittency when you wiggle the tube.
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If you end up using the new CW xfmr, it'd be a good idea to clip out those two resistors before installing it. That way, if the resistors are actually needed, they can be placed externally.
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If it's the primary bad in the old xfmr, it may be re-windable using roughly the same gauge wire and same number of turns.
The primary is untuned, serving only as coupler or 'tickler' to the secondaries, so its exact inductance is not critical.