I did take it up with support and they suggested trashing the mmServerScripts folder from the local site root. I did that and that enabled me to maintain a connection long enough to realize that my mucking about had imposed the 2 following variations:
randomly thus causing me to notice the problem only sometimes.
I think the presence of that difference caused other things to change in an attempt to adapt to my weirdness but I'm not smart enough to know if that's true.
In any event, careful scrutinizing of the entire site and settling on a common definition has seemed to have fixed the problem - for now.
I think the corrupt mmServerScripts folder may have been the incipient cause.
Time will tell.