Weird issue with an RCA 730TV2

[Penthode]

Don't be concerned about the primary and secondary winding resistance. The failure mode of the transformer is leakage between primary and secondary.

Try taking in the replacement transformer.

Other than that, something is causing the oscillator to run fast. I do not think it is a resistor as they tend to drift upward in value. Capacitor leakage can. Check to ensure all the paper dielectric capacitors at oscillator grid including the integrator are replaced.