You could get a tremolo that syncs to audio clicks.
I know of one of these, the discontinued goatkeeper.
Sorry, this probably doesn't seem helpful, but there has to be more than one tremolo that does this.
Does the empress tremolo2 have this capability? I feel like it does.
There are lots of ways to convert various signal to other mediums tap to midi, audio to cv, cv to midi; but no matter what there has to be some kind of source that's keeping a beat. For instance a four on the floor bass drum signal can be run into the audio sync. Or do what I did and give your drummer a tap tempo box and put that responsibility on him. Then you have someone to blame.