It's not an official church thing by any means, but our stake uses the Marquee feature in VLC, and we control it via a simple TCP connection. One of our previous Stake Techs (known as
cboling on this forum) wrote VLyriC -- a program to handle the TCP connection and simplify the process of utilizing VLC.
Our stake isn't spread out enough to need webcasting, so I don't know what to recommend for combining this with a webcast setup, but the links below may have some ideas regarding that...
Here is his topic in the LDS Tech Forums.
This is the page on his site about our setup.
Because he now has (an)other calling(s) and isn't particularly available to continue development/up-keep on the program, I volunteered to do so, at least until I leave on my mission (and probably afterwards, too). The only issue is that he wrote it in Delphi 5 -- which I'm unfamiliar with -- so I'm currently re-writing it in C#. I'll post an update here when I'm finished, and
cboling said he'll update his site with my version if it's good. (Encouragement to do my best, right?

)
Edit: It seems that some of the 'required' marquee features were broken in VLC 2.1.x, so we currently have VLC 2.0.8 on a Windows laptop. I'd like to install 2.0.9, but I'm not having too much luck finding the installer for it. Unless I find 2.0.9, the installer for 2.0.8 will be available in the new VLyriC.