I agree with Ron. Everything you have submitted seems to suggest an issue with your mDNS daemon; not with mt-daapd. While we are certainly willing to assist with getting mt-daapd up and running on your network, in this instance it would appear the problem lies outside the realm of the project’s control.
My experience with getting Wine up and running reliably has been mixed. Too many of the more robust Windows applications require the use of resources which Wine cannot adequately accommodate. For me it has been attempts to get it running on FreeBSD and Darwin systems; Linux may be another issue entirely. Nevertheless, I do not think you will find it a panacea.
That said, if you can get iTunes running under Wine, my agreement with Ron as to your likelihood for success is mixed. If it works, then great! I would posit, though, that such a result would not necessarily be indicative of anything more definitive than the built-in DAAP server within iTunes being properly configured for use with that specific application. Even so, you would still be constrained by the limitations of that implementation.
OTOH, if the DAAP share remains invisible on your network, then it will pretty much guarantee that the issue has been with the network interface on your server all along.
I certainly wish you Good Luck and would entreat you to report back with your results — regardless of the outcome. We can all learn from the success or failure.