ok,
now we know that the VCO section works normally without the mirror board in.
the reason i had you do it this way was to eliminate a few possible voltage paths.
next test is to put the mirror board back in, and do the exact same tests on both radios.
if the VCO freq does start drifting around with the mic gain up, or when you speak into the mic; then we know that you are pulling the supply voltage down, and causing this issue.
the first place i would look is the collector of Q37. its the TO-220 style transistor mounted to the chassis toward the front of the radio from the audio chip.
put your DC voltmeter on the collector, mirror board in, key the radio, talk into the mic, and see if this voltage drops or fluctuates.
if it doesn't then i need to start over and re-assess my advice.
if it does act strangely, then move the positive lead over to the emitter leg, and see if that voltage drops or fluctuates with modulation.
if only the output of Q37 drops, then it is your culprit and might benefit from an upgrade.
(check to see if they used a different part in the "bad" radio, as opposed to the "good" radio)
if the input to Q37 drops also, then either T1, or the power switch isn't up to the task.
if this is the case, then there are a couple of things you can try, but it may end up being a case of that radio just not being able to handle the increase output.
just out of curiosity, what are you running the deadkey at?
LC
