I believe it’s the opposite, that the 6.6k primary will give your more power, which isn’t exactly the same as headroom but prob would be perceived that way. Have you checked out the amp recently? Tested voltages, connections, etc? Or maybe try swapping some tubes. If it had more headroom before something changed, but would strongly doubt it has anything to do with the OT. May want to try a grid stopper on the phase inverter. I just built a Princeton and Rob’s mods were very helpful to me. I did these:
pI grid stopper (470k-1M)
Power section mods (ala deluxe)
Trimmed low end with bypass caps
Stokes mod
20w OT from Allen
Has plenty of headroom. More than my other 18 watt amps. Hangs with a deluxe easy.
https://robrobinette.com/AA1164_Princeton_Reverb.htmI’d also give a few other disclaimers/comments fwiw...
1. my Princeton starts to break up at 5-6 with single coils. Most do in my experience. That would include other blackface fender models too.
2. Per the above, I’ve never heard Princetons being known for clean headroom. Usually the opposite. If 5-6 on the volume dial isn’t enough, speaker and transformer upgrades are the way to go. Which you’ve done.
3. Assuming all is healthy with your amp, you may just need more headroom than an upgraded 6V6 Princeton can provide. Would try 6L6’s since you have the iron to support it.