Sorted it. The Networking Setup utilities in Mepis are as cr@p as the ones that come with most other flavours of Linux.
In the end, I edited smb.conf manually, and all is now accling as it should.
Fortunately, I'd kept notes of the changes I'd made with Debian (all those years ago) to get it to work as part of a Windows local area network with disk and file sharing.
That done, it's good. Most stuff is easier to configure than in previous Linuxes. Only the SCSI DVD drive and the Midi are still not working. Mepis probably is newer than SCSI, and who uses Midi these days...