Hold on, I think I have fixed it. ...
I have found that the heater wires were reversed between the two 6V6s. That is green wire from V4 pin 2 was going to pin 7 of V3 instead of pin 2 and vice versa. Do you think this could have been the culprit? The amp seems to have cleaned up a lot and the notes are less farty, especially in the high inputs, not so much in the low inputs. ...
I highly doubt the "phasing" was the issue.
PERSONAL OPINION ALERT: I think "heater phasing" is a tremendous load of crap. I've built amps both ways (obsessing over heater wiring, and also doing "wherever the wire lands" and each way worked the same for me). I can't hear a difference between them.
I'd bet big money you repaired a cold solder joint in the heater wiring when you made the swap. The cold joint may have reduced the heater voltage, and impacted the amp's operation. You didn't happen to measure heater voltage in the beginning, did you?
Reduced heater voltage (like ~4vac instead of 6.3vac) can cause odd problems in output tubes, reduced power output and may cause strangeness in preamp tubes. In general, gain and Gm lowers, rp probably rises, emission is low, and there's a chance the tube could distort early depending on exactly where the voltage lands and how strong the tubes were to start. Kind of like cutting the power on an amp and continuing to play while the caps drain.
I think you did everything right, and I wouldn't have thought to check heater wiring early, so maybe we all learned a lesson.