Should I install screen resistors and if so, what size? And would this affect the tone appreciably?Tone? No.
Power? Maybe...
With screen resistors, think power not tone. The control grid, G1, has the most impact on plate current, meaning a small voltage change results in a big plate current change. The screen grid, G2, is the second most-effective controller of plate current.
The screen also passes current, and when the plate current is large, some of that current strikes the screen grid and so screen current typically increases somewhat when plate current goes up. If you slap a
large resistor in series with the screen, the change in screen current during high power peaks will result in a significant change in screen voltage, due to voltage dropped across the screen resistor (in accordance with ohm's law).
Another way to think of this is reducing the screen voltage will ultimately reduce the peak plate current possible from the tube. Reduced peak current = reduced maximum output power.
Check out the
7591 data sheet, and look at Typical Operation, Pentode Operation, Class AB1. Pay attention to how much the screen current changes from no-signal to max signal input to G1. The values of current are for 2 tubes, so cut each in half. Zero-signal screen current is 5.5mA and max-signal screen current is 13.5mA for the condition with 400v on the plate.
Now look at the lower chart on Page 3. It shows plate current with changing screen voltage, all while holding G1 at 0v. This is showing how your peak plate current (which peaks when the incoming signal is positive by the same amount that the bias is negative, momentarily driving G1 to 0v) is affected by the screen voltage. Depending on exactly where you look, a 50v reduction in screen voltage results in a 40-50mA reduction in peak plate current.
So we don't want the change in screen current to knock the screen voltage down enough to zap power. We have a change indicated by the typical condition of 8mA from no-power to full-power, and 50v of change on the screen grid is going to be very noticeable. 50v / 0.008A = 6250 ohms. So don't use a screen resistor that big. We haven't quantified how much power output is lost, and I'll save that for another time. But if you used a 2-3k screen resistor, it would probably be a noticeable compression effect and less total output power, but not as bad as 6k.
Also notice that all old amps typically used no screen resistor, 100 ohms, 470 ohms or 1k, depending on the tube type and conditions. When used, the screen resistor was sized just big enough to provide some protection against over-dissipation or some grid-stopper effect, but small enough to not cause an appreciable change in screen voltage.
Depeding on your sonic goals, you could use a small resistor like 470 ohms or a big one like 2-3k. The choice is between no-sag and full power, or reduced power and audible sag.