Today's Mystery Guest (RCA CTC-4)

[old_coot88]

By sheer elimination, it begins to look like maybe the resonance point of the L42/C213 tank circuit is too far off from 3.58 to allow oscillation.

Do you have a signal genny that's reasonably well calibrated, and can be manually swept thru 3.58mc? If so, you might try sweeping the tank and watch for the resonant point on the scope.
(But first disconnect the tank from the tube cathode and C209. Connect the genny and scope to the top of the tank.)