What are the voltages on the 7247 pins 6 and 8 (plate and cathode)? You may be simply running out of signal "headroom" in the VA stage.
The voltage across the 1K VA stage's cathode resistor will be the major input-signal-voltage limiting factor here. I'm guessing the stage has
a 0.4 to 0.7 mA cathode current, (with the 150 and 270K resistors in series with the plate) which translates to 0.4 to 0.7 V across the RK,
and that means that any input voltages above that level, will be clipped, before it reaches the PI stage's grid.
For the 7591s you may need more signal gain than the triode stage can supply, the 7247 is sufficient for the ST35, as it needs to deliver only approx
+/- 14V pk-pk to the EL84 control grids, and the 7591 would be running only about 40 to 50% of maximum power output with 21V (or 20-30% with 14V).
Closer to +/- 28 to 32V pk would be required to achieve full power with 7591s.
The PI stage (pins 1, 2, 3) has only a gain of 1, or slightly less, changing it to a higher gain triode wouldn't develop any higher gain in that stage.
It is essentially a "split" cathode follower, which means it has no voltage gain, though it can have current gain.
A 12AX7 "drop in" wouldn't be advisable, with the PI stage's 22K RA and RK, the maximum safe plate current would be significantly exceeded.
You may have to use a pentode for the first VA gain stage, as is done with the 7868 (similar to 7591 and 6GM5) amp design,
in the back section of the RCA tube handbook.
Plan "B", which would be a major re-design, would be to use the triode gain stage, followed by a Schmidt or similar LTPI,
like Shannon's Poseidon or ST-70 driver. That circuit uses all triodes, and has more than enough overall gain to drive the 7951s. .
HTH
/ed B