So, good news and bad news.
Good news first: I put a 470R resistor in series with the diode (as per @Paul Running
) and it seems to have tamed both the hum and the negative voltage. I am now getting between -28VDC and -30VDC. I won't try to do better than that!
The bad news: I swapped the power tubes and it's not the tubes. I'm still getting some red plating on the second power tube (which I believe on would call V5 if one were to annotate the 5G9 Fender drawing). Not sure what might be causing this - it's odd.
Is it possible that the artificial CT that I am running off of that socket might be causing the issue? The 470 R screen resistor is almost spot-on and seem solid on the meter. The voltage is a bit high - between 390 and 405 VDC. So, yes, higher than the 368 VDC called for in the schem.