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At this point I believe it's Steam.  Why? Because Steam is the only thing that has had an update in last few days - very close to when my problem started. I've been using MO 1.2.18 since it came out (a month or so ago maybe???) and it's been working fine.
 
On top of that, I found this MO's Nexus page, user "Dwailing" has a workaround that worked for me - full normal load order.  It's all about timing though.
 
The workaround:  Shutdown Steam. Start Skyrim from MO. It will complain about Steam not running.  Tell MO to start Steam. As soon as that happens, MO will give you another window that asks you to click "OK" when Steam is started.  DON'T WAIT from for Steam to start, IMMEDIATELY click OK.
 
Doing that has my normal full load working again.  It's tricky because of the timing, but it does prove there's nothing wrong Skyrim, MO, the number of mods or the mods themselves. It's something in Steam.
 
I just hope Steam gets this fixed soon!!!

Welp, that didn't work.  But I DID find the solution. Apparently The Eyes of Beauty - Dawnguard includes a plugin called "babette.esp".  If this plugin is in your load order, it will cause ASIS (at least version 1.42.5, the latest as of this writing) to fail with the error I was getting.

Guys, never mind.  I've basically given up on my current installation.  I'm going to start fresh.
 
What convinced me?  When I went to the "Vanilla Skyrim" profile and started it, the trip in wagon was a physics nightmare.  Cart sideways, Gen Tullis ran over by a cart, half of the scenery missing.  It's not worth trying to salvage this.  I've got Steam verifing local files now and will start over tomorrow.
 
I couldn't find a way to delete my post or I would have.  Sorry to waste everyone's time.

Never mind.  I found the answer in the first few paragraphs of the wiki page: