Years ago there was a mixture control system called "carb smart" by a British company "csm"
It had a temperature sensor that you would glue in the engine head fins.
Simplified it would make the engine run richer if it got to hot and leaner when to cold by turning the high speed needle with a servo.
Tried one but never got it to work well mainly because i run low nitro fuel that makes the engine run hotter then with more nitro.
OS also used to sell (or might still do) a replacement needle that has the lever already build in.
So there is some history of controlling engine mixture remotely if with a relative primitive system.

Since then servo performance has improved a lot. Especially servo's intended for helicopter tail rotor control have become both fast and precise.
If you enjoy experimenting and do not mind "wasting" a bit on buying a tail rotor servo to control your main needle .
Make sure there is no play in the link between the servo and the needle. (use ball joint and a stiff push-rod) and choose a servo with minimal gear play.

What you could try is to divide your throttle "range" in for example 10 steps.
Run the engine test setup and for each of those steps on your transmitter adjust the mixture for a good running engine at that position.
Create a mixing curve on your transmitter using the result of your test.
You might end up with a "mechanical" version of the mixture control system.

Would it work? no idea; electronic will be faster and likely more accurate then the servo needle control system.
But it might be "good enough" and the only way to know is to try.