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Do I need to increase the load resistors (two 56K resistors) on the PI to provide more P-P swing for the 6L6s?If the amp is well-designed, you don't change the G2 voltage, you don't radically change the operating mode from near-A to near-B: no. Both 6L6 and 6V6 have
Mu near 10. Therefore if G2 voltage is the same, G1 voltage will be very similar.
You get more power with 6L6 _IF_ you also lower the load impedance (and have enough power supply). You are leaving all the voltages the same, but increasing currents.
That said....
AA1164 is not "well designed" in an engineering sense.
Skipping to the real-world: I think HBP nailed it. The Princeton always had an identity problem. It was supposed to fill a gap between Champ and DeLuxe. First it was a one-6V6 Champ with a big box. Not too exciting, hardly worth the higher price. The next version was a two-6V6 amp; there's nothing in-between worth building. But two-6V6 is a DeLuxe, and a steady seller. How to keep the 2-6V6 Princeton from stealing DeLuxe sales?
Follow HBP's analysis and then look at the AA1164's B+ rail.
18K?? Where the heck did 18K dropping resistors come from?
I bet they mocked-up a cut-down Princeton with the handy DeLuxe PT/OT, and realized the dang thing was "too good", would steal DeLuxe sales. So they strangled it. Two 10K droppers didn't hurt it much, two 33K made it too lame, even two 22K was lame, but two 18K (36K total) was "just right".
(I still wonder why not 15K+22K.... standard values which may have already been in the bins. No matter.)
If you want the Princeton sound, where the driver can barely drive the power tubes, do nothing. It will barely-drive 6L6 about the same as it barely-drives 6V6.
If you really want Princeton simplicity with DeLuxe authority, change-down those B+ droppers, get more B+ at the driver. Two 10K, two 4K7.... I see AA1172 used 2K2 and 10K (12K total), and takes its driver voltage at the 2K2 tap (it is also a different driver).
I see that 1172 shows 16u caps and 1164 shows 20u caps... this is probably more about RETMA "rational values" fashion-change than engineering. 1172 also uses a choke, but the 1164's 1K resistor only drops 20V so that's not a big factor. The choke may give modestly lower hum, noticeably less cost, more weight/heft. It's an obvious place to save a buck, and I doubt the decision had anything to do with "tone" (except that a slight hum in Princeton gives a reason to charge more for DeLuxe).
All the modern (post 1936) audio power pentodes can make full output if the driver supply voltage is "near" the G2 voltage. That was a key design goal. (Triodes and older pentodes might need driver supply +higher+ than power-stage supply, which is awkward.)
"Near G2 voltage" is vague. If driver B+ is 80% of output stage G2 voltage, that's fine. If driver B+ is half of output stage G2 voltage, that's maybe not enough. AA1164 has driver at 60% of power G2 voltage.... that's dubious. You could probably get more "undistorted maximum power output" with a higher driver B+.
Of course a "barely good enough" driver may be a flaw or a feature.
And if it is a "feature", the exact amount of "barely good enough" may be open to musical taste and preference. Experiment!
If the goals is maximum driver signal voltage for a given load, B+, and tube, you can quickly compute an optimum plate resistor. Here, 230K (two 115K). But getting a good bias is tedious.
Don't bother, someone did this already. The amplifier table in a good tube datasheet will tell you what's "best". In this case, the split-load Cathodyne may be un-split to a plate loaded amplifier with 2*220K= 440K load. The GE tables have suggestions for 240K and 510K, 510K is pretty close to 440K. The maximum Eo for 510K load is for a 240K plate resistor (mighty close to the calculated 230K). Use a 2300 cathode bias resistor. With a 300V supply this will give 47Vrms or 66V peak.
Our 440K load is a little smaller than 510K, so we might pencil 207K and 2,200.
Re-split as a Cathodyne this is two 103K (use 100K) resistors with say 2K2 bias. Expect 33V peak output with 300V supply.
This is not like Fender's two 56K. That would be more like the table's 100K resistors. The table does not have data for 440K/510K load, but in 240K this does 40Vrms 56V peak. Less than the optimum but not a lot less. (And we've already guessed that this design was NOT supposed to be "best possible" but "just good enuff for the price.)