Try it and listen to the amp. Do you like the result? If so, the 2.2k is fine.
I think I (re-)discovered a wrong way to build an output stage a while back, and suggested it to others as a way to add sag. If you want every last watt from your amp, you want as little impedance between a tube screen and its power supply as possible.
The maximum plate current that the tube can pass is governed by screen voltage. If the screen voltage drops (think 10's of volts, rather than 1-2 volts), then the maximum plate current from the tube is reduced. As an output tube transitions from no output to full output, the screen current rises. If you insert some resistance between the power supply and the screen, then ohm's law tells you that as the screen current rises, the voltage drop across the screen resistor gets bigger, and the resulting voltage at the screen drops.
If the drop in screen voltage is significant, then the power output from the tube (plate voltage swing times plate current swing) will drop.
If you must have zero compression and every last watt from your design, you use no series resistor to the screen. Quite a few old hi-fi amps didn't use series screen resistors, but rather used a single common resistor feeding screens on both sides of the push-pull output. The idea was that the rise in screen current on one side would be offset by the drop in screen current on the other side, and result in a steadier screen voltage. Reality is that the screen voltage is steadier, but the screen current do not change in equal and opposite directions.
But protection against excessive screen dissipation is also important, especially if you whack the snot out of the output tubes to get your distortion sound. Screen current increases sharply when you drive the control grid positive. So you'll see production amps with the smallest screen resistor they can use and still provide some degree of screen protection, in order to make all the output power possible. However, if you can accept some degree of compression and a slight maximum volume loss, you can increase the screen resistor value well over the typical values. Some folks around here routinely use a screen resistor around 2.2-3.3k.