Have you ever used a separate speaker selector unit to audition speakers? Would you?

Anyone concerned about not being able to compare or judge because they will forget what they heard in a few minutes should stop and think about that. Ask yourself, if you really can't remember, then why would you care?

That isn't the issue, the problem is you have no music in the hour(s) that wait for the tube amp to cool down and warm up.
A high quantity speaker A/B switcher is the solution, but you have to make sure the tube amp output is connected to a load at all time while power on.
A safe way to swap is mute the input, if the switcher is on speaker A, select A+B first then change to speaker B, so the tube amp will be loaded while swapping speakers.

@miller My effort to find a way to do careful and detailed analyses of complex phenomena does not stem from my inability to "think it through." Rather than imply I'm being obtuse, you could either just report that *you* never needed to do or perhaps suggest ways that you compare things.

Ask yourself, if you really can't remember, then why would you care? If you have no memory of something better, how can anything be worse? Seriously. Think it through. Why would you care?

Yes, one possibility here is that I'm just stupid. But another is that you tend to rush through experiences or don't pay enough attention to realize they are complex. To a gourmand, all food can be gobbled up quickly. But I've read other comments you've made in other places and know that you are a careful listener. Why not draw on that experience and contribute something you've learned to this topic rather than finding a way to demean the question -- and the questioner? 

I would be more concerned about placement than switching. I recently tried my old speakers again after setting up new ones for the last several weeks to try out. The new ones ended up set a littler wider with less toe in but about the same distance from the wall so I thought maybe I could sneak the old ones just inside of them and it would be about the way they were. Either I was wearing rose colored earplugs when thinking back to how they old speakers sounded or the placement was more of an issue than waiting 5 minutes and crawling around on the floor to change the cables over. To position them correctly I would need to move the new speakers, but since this was just supposed to be a quick check to remind myself of some of the differences it wasn't worth the effort to me.

I think I'm cured of trying to setup 2 sets of speakers at a time to compare them. The potential damage to amps or switchbox noise is really secondary.  

+1 re. @b_limo  and @cat_doorman 's point on speaker placement.

@david_ten and @catdoorman - I was thinking I'd just pop one set off the stands, put them on the floor, and put set #2 on the stands in their place. Exact same placement for the comparison. Perhaps different speakers need different placements -- granted. In that case, I'd have a second set of stands ready to go.