Here’s an untested idea, a chopper tremolo using a 555 timer. The idea is to switch on/off only the audio and not the DC bias of the jfet.
the switch with the 555 is a wavefrom selector , at the third pin you get a square (Vcc or ground) , at the sixth a Ramp . The circuit will also work with a BJT transistor but as I uderstand it will saturate quicker. I’m not sure about the JFET switching , I’ve some serious reading to do about this kind of electronic switching.
I’ve also seen an intersting idea with a CMOS gate (CD4069 or something like this) for the same purpose.