First: WHY do you care about pentode plate resistance? In any practical *audio* amplifier the internal plate resistance will be far larger than the DC feed resistor or the load impedance.
> note that rp increases when Eg2 is lowered
But also Current is decreasing, thus Gm is decreasing.
Figure Vg2 does the same thing as Vg1, only less. The two together set the cathode current (Vp hardly matters above the knee).
I would suspect that, like a triode, Mu is fairly constant over a wide range of conditions.
In a simple triode, Mu can be measured with a ruler, simple geometry.
In a tet/pentode there are two geometries (G1 G2) in cascade to measure, and "small" deviations from perfection may multiply to real deviation. And we know plate-lines are generally not flat, but convex upward, so Rp must drop as Vp drops toward the knee. Still I think constant Mu is a fair assumption over most of the useful range.
So taking Dave's new figures, cathode impedance is 1.224uMho or 820 Ohms, Rp is 583K, Mu will tend to be 711. If you shift Vg1 *or* Vg2 to arrive at a different operating current, Gm will obviously change. For small change, Gm varies nearly as square-root of cathode current. (This is not the ideal theoretical result, but most commercial tubes follow the square-root trend well.) So if you run 2X the current, Gm will rise to 1.730uMho and Rp will fall to about 412K. But to get 2X the current with the same supply voltage, you have to cut the DC feed resistor in half. So tube Rp is even less significant.
If you are *really* asking how to maximize nominal voltage gain:
Run very low Vg2 and very low current with large plate feed resistor.
You find plate resistors as large as 1Meg in some DC regulator error amps.
We don't go that high in audio because stray wiring capacitance sucks-out the highs.
Also (and for the same reason) our loads are never >1Meg.
Note that the RCA uses one value at V1, which works alone, and a higher value at V2, which is inside a strong NFB loop which tends to correct a little droop at the high frequencies.
So pick the highest allowed plate resistor, considering load and strays.
Mock it up.
Set Vg1 to zero (tube hard on).
Increase Vg2 until plate just comes off bottom. i.e. zero Vg1 is just enough to bottom the plate, for that supply and that plate resistor.
Now apply Vg1 until the plate is roughly halfway up the supply voltage. Don't go low, thinking high Ik means high Gm. The reduction in Rp will eat much of the apparent increase of Gm.
That will be nearly the highest voltage gain possible for that impedance level and supply voltage.
You may think that adding a buffer allows much higher impedance and thus gain. This is true; but most useful buffers can be used as amplifiers, and usually a 2-stage amp will beat 1 stage plus buffer.
Same argument for most active current "sources".
It should also be noted that two sections 12AX7 will beat any single pentode, for small added cost.