As others have mentioned, it is not the power cable. Also tubes are surprisingly robust and will tolerate more abuse than any MOSFET.
You could use a PC that's has a greater cross-section than 10AWG without any problems, in fact could reasonably expect a slight improvement, the amp will only use the power that is being demanded but there could be a capacitor in the power supply that is going/gone faulty and pulling more current (amps) than the protection circuitry allows. I have experienced a similar problem with the PSU bleed resistor going low ohms.
Perhaps do a visual inspection of the power caps, they will be positioned close to the power transformer, and look for any dicscolouration, swelling or residual smell.
You have already received probably the best advice: Contacting McIntosh would be the sensible thing to do.