The OT is 4000ohms primary but it has several secondary taps, so I intended to still use 6V6s and compensate the ratio by pluging the amp into a 8ohms speaker using the 16ohm tap.
You'll need to apply 8 ohms to the 4 ohm tap to reflect 8k to the primary, but you probably just mis-typed that.
Let's assume your transformers are spot-on replicas of the original Vibrolux Reverb transformers. The blackface Princeton Reverb had a 340-0-340v PT and a 5U4 rectifier, where the Vibrolux Reverb had a 315-0-315v PT and a GZ34 rectifier.
Assuming US voltages, 315/110 = 2.864 * 120v = 343.7v. So happily, applying modern wall voltage to an accurate Vibrolux PT results in old-style secondary voltage perfectly suited for a Princeton Reverb. Though you might see some variation on the proper rectifier for the PR, I always used a 5U4 in mine; my first tube amp was a '67 Princeton Reverb, and that was the specified rectifier in that amp.
I agree with 6BQ5 that much of the Princeton character will be retained by the power supply and phase inverter style. And original blackface Princeton's used a Jensen C10Q speaker. Don't use a "too-good" speaker that has a bigger, clearer sound than the original, and you'll be fine. I haven't done a speaker shoot-out, but the reissue Jensen C10Q sounded reasonably close to originals to me, after some break-in. I've used maybe 3 C10Q's in the past. They're not 100% the same, but a new speaker will have a hard time matching a 40-yr old original. And you can't beat the price of the reissues.