... high Z out is followed a relatively low Z in, but being able to source more current to drive the voltage swings. ...
A grid that is not driven to or beyond an instantaneous 0v (i.e., not drawing grid current) could be considered a near infinite input impedance. So the only thing that lowers it is the grid reference resistor (which are generally limited to about 220k or so because that is what tube manufacturers specify). However, that does not apply in the case of the tremolo or bias circuits, because they are not impedances to ground, but like wires to an open circuit (the grid).
I'm thinking the issue may be a result of bias-shift caused by the rectification effect of the output stage. This is where the d.c. voltage (bias) changes when a signal is applied, and because it's a d.c. change with an applied signal it is described as rectification.
Regardless, step back from your theory for a second. If it was true that the cathode bias is opposing the trem signal, how is the
guitar signal causing an output to occur?
Now, maybe we could say the cathode bypass cap (if used) is not big enough to be an effective bypass down to a couple-Hz where the trem signal is, and that the local negative feedback of the cathode resistor is coming into play.
If that is the cause of the apparent reduced trem strength (assuming it's happening), couldn't you look at other bypass caps or other methods to bias the tube that have no feedback down below 1Hz?
By "other methods" I'm thinking either resorting to solid-state to define the bias voltage, or the old-school d.c. heating of some preamp tubes by placing their heaters in series between the output tube cathode and ground. That second method is tricky, because you have to need something like 25.2v bias while the tubes idle at 150mA (for 2x 12A_7 tubes with heaters wired in series and using pins 4, 5 only).