My main concerns are plate voltage, negative bias voltage, and OT impedence mismatch.
If you don't want VVR or to pull tubes, then then there's one more thing. The iron will be way over-spec for the lower current draw of the 6V6's. That means a stiff, well-regulated PS, uncommon to guitar amps. No sag & no OT saturation. It's a subjective preference that you may like. Just wanted to point it out.
There's currently 480VDC at the OT center tap. . . Should I try to drop more than 100V for the 6V6's?
420 plate volts for 6V6 seems high, but the Fender does it in the Deluxe Reverb. There's also a brand of 6V6's that can supposedly take about 500V (JJ's ???). Anyway you can shoot for 420V or less.
To guesstimate, I would measure your amp's unloaded plate voltage. Check the Deluxe Reverb's specs for power tube current draw & multiply by 2. Figure the voltage drop in your amp with 4X 6V6's. The measured voltage drop w/ 6L6's may be helpful. Or, maybe use the Duncan PS calculator. Then you'll know how may additional volts to drop with zeners. I think a 100V drop is the practical limit recommended for zeners.
Personally, I would build another amp for a quad of 6V6's, with the right iron. I like to hotrod guitar amps and overwhelm the iron, but not vice-versa.