I'm reading up on cascodes a bit. If I'm understanding correctly, the first triode basically "re-amplifies itself" using it's second triode? I guess the high-gain cascode explains the low-gain 12AU7 for the last gain stage....
In simplest terms: the Cascode is essentially strapping 2 triodes to act as a pentode. Gain for the composite pentode might be much higher than a 12AX7 stage, but it's also much lower than 2x 12AX7 stages in cascade (on after the other). Since it might be simpler (fewer parts) to just use an actual pentode, a designer would need to have some very good reasons to use it. Hence, it's just a curiosity or "because-I-can" in guitar amps.
I guess the high-gain cascode explains the low-gain 12AU7 for the last gain stage....
Amps get designed from output to input, so that's how you should analyze them.
The 6V6 output stage is shown to have 17v from cathode to ground (bias voltage), so maximum design input to the 6V6's was probably ~16v peak. The split-load or cathodyne inverter at the 2nd half of the 12AU7 offers no voltage gain but does have good balance if the output tubes aren't drawing grid current. No-gain there means the split-load needs ~16v peak of input to drive the 6V6's fully.
The 12AU7 gain stage before the split load probably offers a gain around 10-11, so about 1.5v peak would drive the 6V6's fully. But negative feedback is also returned to the cathode of this stage, and it doesn't have a full-size cathode bypass cap, so actual gain from this stage is more like 4-5 and so ~3v peak at this stage's grid will drive the 6V6's to full output.
You want decent sensitivity to your Aux input, but maybe you think a pentode is too noisy or prone to microphonics. So you opt for a cascode to get pentode gain and hope it answers some other issues. A 12AX7 in cascode (not the best tube choice in general for this circuit) might exhibit a gain for the circuit of ~100-120, so input sensitivity for the Aux input is something like 25-30mV for full output from the 6V6's. And to allow for a wide range of Aux levels (which could be well above 30mV), a Volume control sits between the jack and the cascode to prevent the signal from distorting the cascode.
A Mic could require an even higher sensitivity, so we have additional 12AX7 gain stages for each Mic input (gain about 55 for sensitivity of ~0.5mV) with level control again to keep things from distorting later stages.
Or at least, that's how the PA Designer looked at it.