I have a similar setup, but I have Squeezebox Classic players, not Touch.
(And I am using MB v3, which I see you are reluctant to upgrade to)
You could have a look at the UPnP/DNLA plugin.
http://getmusicbee.com/forum/index.php?topic=14277.0It was created by Steven himself, with a lot effort. For many users it seems to work well by now, but using it with Logitech LMS is a different story.
Probably due to the fact that the Squeezebox (Classic) heavily depends on the LMS software to be installed, and seems not to be fully DNLA compatible just on its own.
After lots of trial and error, bug reporting, and tweaks by Steven, the last result I accomplished is that it would work for mp3 files, but not for FLAC files.
(only occasional bursts of loud distortion coming out of the speakers)
So you could try it out yourself, and see how it turns out for your setup, and if you are happy with the results.
Be aware that since that plugin was extremely time-consuming to develop and maintain, development of it is currently on hold.
So don't expect further issues with it being resolved anytime soon.