A couple of things it's a good idea to at least add a series resistor like the Dallas Arbiter Tremolo,
https://viva-analog.com/dallas-arbiter-trem-face-rare-re-build/The transistor needs to work as part of a voltage divider. In the Leyand it's relying on the pickup providing the impedance but it's not going to work well if you place buffered output pedals before it.
As far as your gain restoring circuit goes it needs work. In short just take any non-inverting opamp circuit and put it after the tremollo,
https://www.electrosmash.com/mxr-microampNo doubt you can strip it back a bit.
The main issues with your schematic are:
- The opamp connection has a lot of issues since you are DC coupling the input.
- The inverting scheme doesn't lend itself to the best solution. (It is possible to do a inverting version
but it will be less optimal than the non-inverting.)
- You are taking the 4.5V/Vref line from the oscillator circuit.
It looks like a 4.5V/Vref, and it kind of is, but it's not a Vref suitable to connect to audio.
That 4.5V/Vref is part of the oscillator circuit and works in conjunction with the 220k
resistor feeding back to the opamp + input. The voltage at that point is varying
if you use it for audio it will tick. You can't even add a cap across that Vref to fix it
since it will stop the oscillator.
If you look at the Schaller Tremolo you can see a similar kind of idea which uses a BJT
amplifier to restore the level. It's both similar and different. The colorsound is another one.
IIRC the DIAZ Tremodillo was a another transistor based tremolo.
You can stick to your plan using an opamp.