I suddenly tripped over the answer...
I was looking at the share "names" on that machine, and they were a bit long. "E_Drive_Backup_168," logn but intentionally descriptive. So, just for grins, and somewhat in desperation, I created a new share that was more typical for me and called it "E_Drive." And presto, the Macs could now login. So ... keep those share names short! Apparently there is some limit on share names that does not bother Windows machines but leaves Mac/Samba totally lost.

