Interesting, indeed. As already mentioned, I didn’t test with MusicBox, but I may be able to look into that over the weekend.
BTW, MoMo is looking for the _mopidy-http._tcp ZeroConf service to avoid listing other Web servers in your network, but that should be available on v0.19.5, too.
kimhaak: I was actually interested in whether your MusicBox was found by Mopidy-Mobile’s via ZeroConf. Sorry, should have been more specific.
The system I’m struggling with is not musicbox (the pre-release version I’m using actually comes up fine on MoMo for me), but mopidy on xbian (xbmc distro). It advertises a bunch of additional non-mopidy services but I don’t see why they’d interfere. Since this is slightly off the OP’s topic I’ll come back to you when I’ve had a chance to dig into what I’m getting.
Just in case someone else stumbles upon this thread:
Here is the upgrade procedure, if you are willing to risk a full reinstall if something breaks.
On a side note, for debugging ZeroConf-related problems it may be helpful installing a third-party ZeroConf/Bonjour browser app on your device, and see if Mopidy’s HTTP services are reported. That way, you’ll know whether to blame your server/network configuration or the client app’s author 
I personally use ZeroConf Browser [https://play.google.com/store/apps/details?id=com.melloware.zeroconf&hl=en], but there are a couple of other ZeroConf/Bonjour apps available for free the on Google Play store.
Remotedy is now updated to only show Zeroconf services provided by Mopidy:
_mopidy-http._tcp.local(Remotedy v1.0.14 or later).
I use mopidy-mopify web-addon to control Spotify remotely over mobile etc. It’s quite good, and has a nice UI with (in my eyes) high WAF and full support for playlists and saved albums. You can find it at https://github.com/dirkgroenen/mopidy-mopify 
While all true, OP wants an app.
I had “MPDroid” for my Android and without doubts I am moving to “Mopidy mopify”. Much better and cooler.
(I didn’t like at all “remotedely” though)
Thanks for the suggestion @kingosticks