The APC unit has arrived today.
Unfortunately, the 220/230/240V switch on the back of the unit does not have any effect whatsoever on the output voltage.
What goes in, goes out independent of the switch setting, at least if the input voltage is stable (233V in this case)
(the measurements were not done while idling, but with the amp connected, and the unit was shut down each time before changing the setting)
This means that the device is useless for my purpose, and will be returned.
Today I have purchased the proposed variac in ebay, it should arrive by Saturday the latest.
When it arrives, I will implement the proposed changes and see how it fares.