Freddy, that is an AWESOME build!

Where did you get the lighted switches? Are they LEDs? They look very cool.
As to debugging, your voltage readings suggest that you aren't passing much current through the "bad channels". Your plate voltages are high because of this (not a lot of current, so little voltage drop across the resistor), and your cathode voltages are similarly low for the same reason.
Normally I would suggest that you check your plate resistors as it seems like they might be smaller than what the schemo calls for (i.e. lower resistance yields a smaller voltage drop with the same current), but considering that the unit worked fine to start with but now is distorting, I doubt this is the issue. Still wouldn't hurt to verify that all the plate resistors are in working order and the correct values.
The switching tubes idea is a good one, but it seems hard for me to believe that 5 tubes would go bad that quickly, unless of course your filament voltages are waaay high. So check those too.
A good first test would be to take a tube from a "good" channel and swap it with a tube from a "bad" channel. Fire up the unit with both tubes in place and see if the good and bad channels have switched. If so, your issue is solved. If not, you're possibly looking at some kind of issue with the components or wiring surrounding the plate supply there. I've never done pcb mounted sockets but have heard of issues with bad connections due to heating/vibration as someone else mentioned before.
Also, it might be helpful to see a schematic of how you are supplying the B+ across the 8 channels, there might be some things to look at there but we can't tell you considering that we don't know how you have that set up.
Anyway, that is one fine looking build. Please keep us posted on how the troubleshooting goes, it is always helpful to share this kind of information for future builders.
Mason