Guys - oh my gosh! I've now got two variants of the Intel536ep modems working on separate desktop machines! (The second one definitely has the Ambient 5628D chipset.)
Here's what led to it:
Firstly, wingruntled inspired me to try the modems having booted from the original Mepis 6.0 live CD. They worked! Mepis automatically created a proper /dev/modem link without me needing to tinker in any way with the modem settings.
Secondly, I booted from hard disk again, selecting the original
2.6.15-26-386 kernel instead of my usual updated 2.6.15-27-686 kernel. I then uninstalled the intel536ep-modules-2.6.15-27-686 package and installed the
intel536ep-modules-2.6.15-26-386 package instead.
So, it looks like these modems only work with the original 2.6.15-26-386 kernel!
Thanks for your encouragement and I'm so happy to have got these old "winbrutes" of cards working.
But, looks like I'll probably have to stick with Mepis 6.0 rather than upgrading to 6.5 when it comes out, because of the modems issue and the definite problems I know that I'll have with Matrix G400/G450 and Nvidia Vanta graphics cards. Oh well, back to the tried and trusted old gear!