The reasons why my research is leading me to believe that my original idea wouldn't have been a good fit are:
i) We’d be switching as many as several times a day. That’s a lot of wear and tear on connectors and cable if manually plugging & unplugging each time (to say nothing of accessibility to the rear of components mounted in a rack)
ii) Much of the switching would be done by family members when I'm not around, some of whom are not as careful as I’d like
iii) If I did go with a tube amp, manually unplugging cables would just be too risky. Too much chance of a cable switch being done wrong, resulting in tube gear operating without load. Pow, thousands of dollars of sophisticated gear back to the factory
iv) I’ve found only a few switching boxes that are ostensibly audiophile-grade, and I think all of them -- Van Alstine, Luxman, Adcom, etc., are no longer actively marketed or supported in the U.S. The inexpensive boxes on Amazon -- as well as DIY projects -- are too scary. Like some of you, I might luck out & pick one that works. But there’s just too much risk of dead time between switch positions, pickup noise, sound-altering connectors & internal cabling, or even a fatal manufacturing defect. Don’t laugh about that last concern. 4 or 5 years ago, I bought some inexpensive Pangea speaker cables -- something like $100-200 for 2 meters -- on Amazon. When I plugged them in, no bass. I at first thought that they just needed to be broken in, but it took only another minute of listening to realize that they had been wired out of phase. If something that obvious can slip through the cracks of an off-brand product, even if that product is marketed as "audiophile-friendly," a cold solder joint is hardly out of the question.
I’ve spent so much time, effort, and money carefully selecting each component in my system, all of this falls into the category of "the odds are against it, but the stakes are high." So I’m gonna have to abandon the idea. I'm glad I posted the question in this forum before just barrelling ahead.
The good news is that I’m discovering that a few higher-end integrateds offer functionality that lets me accomplish the same goal that the two-amp-switching solution was intended to. There are other ways to automatically switch signal paths without having two power amplifiers physically connected to the same speakers.
So even though I wound up deciding that what I wanted to do was not the best solution for my specific set-up, I'm far from dead in the water. And the opportunity to discuss this at length with so many knowlegable peers here was a valuable part of my investigation. Thanks, everybody!