Wonder what the "loop" (to J7-2) is doing. There isn't a controller, is there? And what's the tube doing? Seems to be shorting it out when keyed, weird. Or pinging it, but there's no plate supply voltage for that.
Anyway, injecting some reference to T201 or R3 or R4 should do something, assuming the tank has wide enough bandwidth to be pulled as much as needed. A better solution might be power varactors on T202, or even a servo to run a small air variable cap to Q301,,, wait what the hell that's an inductor not a transistor.

In any case, you'd have a PLL against the reference, which is likely to have a wider tuning range and lower noise than injection locking? Not that pulling T202 will do all that much because its output voltage won't be too high a fraction of Q301's, I think.
Note that modulation will pull by a similar amount [as varactors on T202], due to Q203/4 collector capacitance varying with supply voltage.
I would much rather leave the tank to its own devices and time everything else against it..?
Also, I don't get, or know, if this is just an idle question, screwing with an existing machine that likely isn't broke (which as the saying says..), or new design for a mass spec you're making, or...
Tim