These are supplied in pairs, one on 27MHz and one on 40MHz.
Not practical; without finding out about the receiver IC, ABERX69A. Google returns no info.
Changing the crystal to an adjacent channel does change the frequency; as expected. There is nothing to trim.
As a test, I changed the crystal frequency from 27.145MHz to 26.500MHz. The RF output changed accordingly, but the tank was still fully controllable. The receiver is not selective.
This probably explains why they are supplied in pairs, on two quite different frequencies.
The modulation seems to be simple OOK (on-off keyed).
The receiver is not very good. Bandwidth is very wide. It looks like just a front end single transistor amplifier that feeds through a tunable coil to a IC receiver that I cannot find any information on.
Image to the right: red wire is the antenna, 8-pin black chip is part of the receiver.
There is no crystal or external clock. The IC may be quite smart, but I doubt it. Smart would include a internal oscillator-PLL and be programed at the factory to receive a specific frequency.
The simple-basic option is that the IC contains just a untuned amplifier and detector or limiter (a super-regenerative receiver). This uses the input circuit and the tunable coil to set the centre frequency +/- quite a lot. Not very selective, and not allowing adjacent channel rejection. This option means little or no setup in production and lower cost.