Figured this issue out.

We did not have control of the network's router - so the DHCP/DNS was hosted on the router owned by the internet provider.

Because QB clients require access to the server both via IP and hostname, we had to either adjust where the DNS was or edit the host file on the Windows machine. We wound up adjusting the host file on the two broken Windows clients. (Which we had to copy the hosts file from c :\windows\system32\drivers\etc\hosts.file to another location, edit, then copy back & replace existing.)

Once we did this, multi-user mode worked perfectly.