The lower device enhanced current arrangement of the cascode (additional resistor from B+ to lower triode anode) would be the way to go to get the "12AU7'ish" triode current up a bit for more gm.
This method is described in Merlin's Preamp book. Remember that the gain of a cascode is approximately the lower device's gm x the upper device's RL.
You would also want to elevate the heater to say +70V.
Definitely worth a try.