Why can't you drive a tone stack with a pentode? If you can drive it with a 12AX7 triode, you certainly should be able to drive it with a pentode. Will you like the tone? Won't know 'til you try it. You like your Route 66, eh?
I swear that I've seen a schematic with a pentode going into a TMB tone stack and then into a PI. I thought it was a Peavey but can't find it. IIRC the PI was a concertina. IOW another gain stage followed by the actual phase inverter. Now I don't know if a 12AX7 concertina will drive KT66 power tubes, but the low gain/high current side of a 12DW7 might. Again, I know I've seen a 12AU7 concertina PI somewhere. Fixed bias for the concertina and a grid stopper might help get the headroom you need there. See Merlin's site for enhancements to a concertina PI. Also, R,G. Keen has published some work on MOSFETS as power tube drivers...
Guys seem to think the long-tailed PI has more gain. Well, the concertina triode itself has slightly less than unity gain but the stage before it is a perfectly normal gain stage with more gain than an LTPI if I remember right. The downside to the concertina is the potential for nasty distortion when overdriven, Merlin addresses some of that.
One big advantage of using MOSFET (or tube) cathode followerS after the pentodes is that you wouldn't have to worry about mixing resistors before the tone stack. You'd get perfect isolation and greatly reduce the insertion loss from the TMB at the same time.
You know those subminiature dual triodes on the effects loop board make me wonder if that's what's hiding inside your mystery man's circuit - each triode as a cathode follower for one of the pentodes.
Spitballing/daydreaming here: what if one channel uses a pentode and the other parallel 12AX7 triodes Riggs up with a Fat control on one like Tubenit's circuit shown above. That would give you a purpose for the first volume/gain pot you already have and very different tone compared to the pentode.
Hope that helps a bit and isn't pure nonsense,
Chip