I'm going to answer this myself, just because I technically managed to 'fix' it... I might leave it to others to figure out quite how it worked...
The 'fix' - I installed the Creator's Update - Build 15063
This in itself took a lot of juggling. I ran every troubleshooting tool known to man, whether they seemed apropos or not [Click Start, type troubleshooting, hit Enter, on the left select 'see all'... run every single one, as admin if appropriate under the advanced tab for each] many many reboots later...
I also ran Windows All-in-one Repair tool from tweaking.com a lot of times; many times it hung the machine. Many times I had to run chkdsk & try again.
Eventually, the Creator's Update, which had failed several times before, finally stuck.
This 'fixed' my DISM issue, presumably by replacing the catalog it was comparing to.
It also fixed my explorer.exe crash at shutdown.
[I deserve no interwebz points for making this work... it was two days of Google & guess & try & hope & try again]