Well, just spoke with the Marantz guy again (I live in Japan, it's Monday afternoon here). He thinks what's happening here is probably normal. It's just that I didn't have this problem earlier because I lived in apartments where I couldn't crank it up like I can now. And also, my living room is now a decent size while previously it was small. So these speakers are probably just really difficult to drive.
He is quite sure that there is nothing wrong with the amp. They performed load tests on it, and it all looked normal to them. He was adamant that capacitors have nothing to do with this situation. They don't degrade materially in 25 years, according to him. And there are over 100 of them in this amp. Exchanging them all would be ridiculous and highly unlikely to produce any results. On the other hand, if the speakers are of the same age, then some degradation in those might cause premature cut-outs, especially if bass seems to be the issue. Which they are, and which it does.
I can do the measurement you,
@Cbdb2 , suggested next time an electrician comes here. An air conditioner needs to be installed. That will happen in the next few weeks. I can ask the guy to help me with that measurement.
Ultimately though, this probably boils down to getting new speakers. I've been ogling the Wharfedale Diamond 12.3.... If the amp still gives me grief with those, too, I'll have a firm basis for complaint. WhatHifi even tested them with the much less powerful Marantz PM6007 and had no issues.
Thanks to everyone here for your comments!!