I thought I'd chime in and go over what we have done in our Stake Center. Like some others have mentioned in this thread, we are doing HDMI over cat-6. We are using converters from Kanex. It takes in a single HDMI signal, and splits it to 4 ethernet runs. In our building, we feed output from our video switcher to an HDMI splitter, which feeds two of these Kanex transmitters, and the webcast box. In the building, we have run cat-6 to a number of overflow locations, including 1 to the pulpit (more on this in a minute), one at the back of the chapel (feeds to a projector in the center of the cultural hall), 2 to the cultural hall (for projectors on the sides of the cultural hall), the Relief Society Room, Primary room, and another overflow location. The run to the pulpit is fed to a smaller tv (22 inch) that shows the Stake Presidency what is being broadcast. The Kanex hardware works great, even exceeds their specifications. We have a number of runs close to 200 ft, and the video signal is clear and solid. We ran all of our cables (both for these runs, and our camera signal/control) through the crawlspace under the building.
We use the building PA for audio, which I may amend later. Part of the problem is an audio shift that occurs. We feed our camera outputs into a computer with a software video switch. Because of this, the video lags behind the building PA. While not a big deal, it was a bit distracting for those observing in the overflow locations and on the projectors in the cultural hall.
http://www.ramelectronics.net/product.aspx?zpid=1987 - This is the Kanex product we are using. It says distances up to 100 ft, but we are pushing 200 ft with ours and have no issues.