Simplest option for generating audio tones?
This is one of the simpler ways:



Source: https://www.nutsvolts.com/magazine/article/op-amp-cookbook-part-3
Tone control could be done with mosfets switching components (like a parallel cap for C1\C2 (maybe you'd only need one?)

Op amps with the bandwidth you need can be had for the 10c cost range with quantity. Timing would need to be done with a 555 timer. This is probably not the best way, but "a way" to design a circuit like this