Let's think simple.
If you have a trigger edge and you have a fixed width output pulse, then you have duty cycle modulation, just at varying frequency. This is PFM, an alternative to PWM and common in low cost power supplies and resonant types both.
If the electromechanical movement is DC current operated then you might just square up that sensor to bang-bang (CD4009B could handle 18V but not much more, filter & protect) - and custom ICs are no more reliable than their designers made them, with many newbies put to the task in my days as an ASIC "godfather" - maybe this little piggy has a lot of brothers already bacon....
Hex inverter (one for auto-bias, use the single stage type), one-shot (CD4098B?), L-C-R filter and there's your frequency dependent DC current for a torque type movement.
Maybe the clutter is part of the problem. Can you deduce or find the movement's electrical interface attributes to work from, cut out all the middlemen, go from sensor pulse to needle swung in 2 cheap ICs of a size human hands can solder (SOIC-14 or DIP, where does this cobble have to fit?).