Before anything else is done here let's make sure the circuit is correct before proceeding. Going off of the posted schematics it appears that your circuit is missing a couple of things.
Looks like you're also missing the grid leak resistor on stage 2. Usually you would use a 1M gain pot with one side grounded for this between the coupling cap and the grid of the 2nd stage.
The grid leak resistor is part of the cathode bias (or "space charge" bias as you call it). Without it there you have no bias at all. The filament supply references the filament cathodes +1.5V above ground, but without the grid leak resistor the grid has nothing there to pull it to zero and as such is undefined. It has to be pulled to zero via the leak resistor in order to be more negative (less positive) than the cathode filament to develop your space charge.
The other thing it functions as is the load resistor for the driving stage. Without the load resistor there the coupling cap has no way of charging/discharging as plate voltage rises and falls, which is how you develop the output signal in the first place.
Perhaps a better way of doing this -
**broken link removed**
Leave your plate resistors fixed and adjust the drive level via the pot, which also serves as the grid leak for stage 2. The 1st stage coupling cap isolates the pot from the plate voltage.
For higher levels of gain use higher value plate resistors to get a higher swing. If you really wanna go wild with the overdrive add another stage at the front end.
I would also consider dropping the value of your coupling caps. Since these are directly heated cathodes you really have no way to shelve unusable low frequencies via partial bypassing since the cathode filaments are referenced to a fixed voltage by default, and you'll just end up distorting everything...even the bass...and that doesn't sound/feel very good as it gives you the "flubby/farty" lows. As such, this leaves only the coupling caps as your method for shelving bass to keep the lows from getting distorted. For tighter cleaner bass I'd start at 0.0022uF (2n2F) and go down from there.