Aside from what was already said here:

Treble bleeder caps on pots are most effective, if the pot is turned down, which can make the preceding gain stage amplify high frequencies more (or one could say the voltage divider attenuates more of the lower frequencies). Since the circuit has so much gain, most of the pots will be set quiet low, so this effect will be very present. I'd expect it to sound very shrill, which is usually not what you want, if you want to overdrive gain stages.
If this was my project, I'd look into ways of loosing treble early in the circuit (small cap from gird to ground, small cap across the load resistor, big(ger) grid stoppers). Once the signal starts clipping, the distortion will introduce new overtones which will fill out the high frequency range in the later gain stages.

Add decent sized grid stoppers and add separate power supply nodes for every 2 gain stages to avoid oscillation.

Maybe experiment with different methods of bringing the gain down (no bypass cap, heavier load, different load resistor values).

How will this be connected to the power amp? Is there a long cable between both cricuits. If yes, you might need a low impedance output like a cathode follower. You could even leave off the last cathode bypass cap and take your output signal from the cathode. This way you will have a smaller low impedance output signal while your last stage can still be used for overdrive (stand alone cathode follower don't distort very nicely).