400v isn't crazy for 6V6s,
N.B.: By "off the charts" I didn't mean crazy, just literally "off the charts": 400V is not on the 6V6 tube charts. Actually, I have no problem with crazy, off the charts, or both. DIY can open up these possibilities, and a reason why we're here (i.e., on this particular Forum). But there are consequences. The thing is, we can inadvertently drive ourselves to incompatible design goals.
If you want to go the lower B+ voltage route: other than a different Rectifier tube, my formula is: a B+ dropping resistor and/or a 12V CT bucking tranny. With a B+ dropping resistor you can drop up to 50 plate volts. Maybe that alone will work for you, after re-biasing. With a 12V bucking tranny - given your PT multiple of about 4 - you can drop another 48 B+ volts; or with the 6V CT you can drop 24V of B+.
Also, though I love chokes, it's working against your design goal for PA overdrive. The induction of the choke kills ripple, while its low DC resistance keeps screen voltage high under hi signal conditions. High screen voltage keeps plate conductance high, resulting in higher power tube output, more headroom, and less power tube overdrive. That's why I suggested the possibility of larger screen resistors. Under high signal conditions, large value screen resistors will drop screen voltage compared to plate voltage, hence reducing plate conductance. This is another route, within the power amp section, to earlier overdrive.
In sum, the combination of i) high plate voltage, plus ii) a choke followed by small screen stopper resistors that keep screen voltage high under high signal conditions, is incompatible with the goal of easily overdriving these power tubes.