If you can afford losing a bit of frequency stability, you can use a varicap instead and control it by voltage. Precise multiturn potentiometers are much cheaper. Or just buy a programmable clock signal generator based on PLL and then make it into a superhet (you can still have analog filtering and detection, but digital frequency synthesis so it can look more like a modern radio with frequency display).
There are so many options and all are very cool to explore.
> There are so many options and all are very cool to explore.
Very much agree, controlling a varicap via an MCU is a nice intermediate step of "digital tuning" without going all the way to SDR.
Yes, varicaps are good and there are even varicaps with very large capacitance swings exactly for this purpose.
But it does require a very steady voltage and many more parts than just a single passive to not accidentally load the resonant circuit to the point that it becomes ineffective. You need to de-couple considerably to make this work, especially without injecting (phase) noise. And frequency stability and phase noise can be extremely annoying in particular applications.