YES!
I had not realised I needed to copy the encrypted output string from FOGCrypt.exe to the web-based UI. It joined the domain after a few seconds of sitting at the login screen without intervention.
Thank you SO MUCH for the responsiveness and help. You guys rock. It looks like I’m going to trash the Acronis Snap Deploy. So far, FOG is better.
Thought I’d add a follow-up.
@Wayne-Workman - many thanks for the recommendation of Debian and for the https://wiki.fogproject.org/wiki/index.php?title=Debian_8 link.
I’m back to two working FOG servers (one for each domain/subnet) and got a nice bonus: With the Ubuntu servers, Veeam Backup and Replication wouldn’t do a VeeamZIP job on the server, only on its replica (which made backups on the host with the replicas much longer than the host to the FOG servers. But the Debian servers can have a VeeamZIP job done on them, so now my nightly backups are much more balanced. 
Thanks, again to @Tom-Elliott and @Wayne-Workman for the help. I really appreciate it. You guys rock.