... a very quick clip I just made of how the trem sounds. ... this emphasizes the motorboating that occurs at fast speed. ...
That's not motorboating, or at least doesn't sound the way that low-frequency oscillation through the power supply (which is termed "motorboating" due to the putt-putt-putt) sounds.
What you have is a byproduct of the VibroChamp-style trem, and a speaker with some bass response.
The reason this particular trem circuit is not used on bigger amps is that the way it's injected at a preamp cathode will cause you to hear pulsing through the speaker, even without you playing. Much of the development of tremolo circuits was about getting rid of this pulsing, including the circuit in the tweed Tremolux, which Fender patented. The tweed Vibrolux also had a circuit to cancel the pulsing, by applying the trem to modulate the bias of a push-pull output stage.
But the VibroChamp was a student-level amp, with an 8" speaker in a tiny cabinet with relatively little bass response. The relative lack of low end helped mitigate the problem, while the "student-level" status set the bar lower. It would appear Fender "devolved" their trem circuit to add this feature to a low-cost amp in their line.
All of the VibroChamps I owned had some amount of pulsing background noise, mostly from hiss in the amp. I think your case is more noticeable because of the added bass response of your speaker.
One thing I like about this tremolo which the modelling amp designers never incorporate is that the tremolo, when engaged, gives you a louder signal than the straight one. Maybe this is caused by the load it places on the circuit even when it's not in use ...
Not a load in this case.
Rather, the trem signal both subtracts from
and adds to the bias of the stage it's injected at. So you're right to say it makes the amp louder when turned on; softer too, but you notice the louder part. Of course, that's how the trem works by turning the volume up and down. The simpler optoisolator trem doesn't turn the volume up because it can only shunt the signal to ground.
There seems to be another issue now, though. When I turn off the trem with the switch (no pop now) and have the Depth setting at full (which is where you'd usually have it) the amp's volume is too low. If I turn the depth pot down while the trem is still switched off the volume comes back up to full.
If I don't use the switch at all and just control things with the Depth pot everything seems fine.
I've long since sold my VibroChamps. Maybe a current owner can see if the same thing happens with theirs. I never had that issue, and don't see a ready mechanism for a properly-wired amp to do that, but I also never used the footswitch with those amps. I just turned the Intensity pot up and down with no footswitch.
Try this... Disconnect the wire from the ungrounded side of the depth pot. Connect a .1µF cap to that terminal. Connect the wire to the other end of the cap. IOW, put a cap between the pot and the wire going to the tube.
He can't do this without removing his 5uF bypass cap. The 0.1uF cap will form an a.c. voltage divider with the 5uF cap and reduce the trem signal at the V2a cathode to almost nil.
So, try lifting one leg of the 5uF cap temporarily to see if the trem issues are fixed, and you can live with the loss of dry gain.
If the trem winds up working, but you
have to have the extra gain, you could probably use a 50uF (maybe 25v or so) cap, with the positive end towards the Depth pot and the negative towards the tube cathode you're injecting the trem at.