I still find it amazing that the variac is showing a consistent 120 volts as set by my original dial setting.
If you have a descent true RMS DVM meter you should check the voltage at the receptacle the amp is plugged into at start-up. That will tell you what the true voltage drop (VD) caused by the inrush current draw of the primary winding of the power transformer of the amp.
Next voltage reading to measure is with the amp loaded. That is with music playing, volume set to where you normally listen. Play something with lots of dynamics.
Measure the voltage... If the voltage is fluctuating in rhythm with the music that will tell you the variac is voltage/current limiting. To verify the variac is causing the VD repeat the same test with the DVM at the wall receptacle the variac is plugged into.
Dynamics performance of the amp will suffer.
Your amp should sound best connected to a dedicated 20 amp branch circuit without being restricted, choked, by the variac.
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