Well, the stress testing of the MPEG-2 player is finally underway. I started a playlist last night that runs approximately one hour and put it into a loop. I decided to try VLC Player again, and oddly enough, it worked without any stuttering or freezing. In fact, I've decided that I'm going with it again, at least for the time being, in the MPEG-2 player. I hope to be stress testing it for over the next several days to see how it's going to hold up.
I think the reason it didn't seem to be working properly the first time was that I may have had Windows configured to download and install updates as they became available. This, of course, is problematic. I've now got this configured to be done once a week, when the feed will be taken off-line anyway due to maintenance, like how a regular TV station would operate. As a result, VLC runs nice and smooth right now. The films I'm using with the testing, my first episode of ironically titled "The Catholic Hour" (Total Running Time: 30 min), "Our Lady's Shrine", and "Rome: The Sacred City" among others, so far have looked like I was running these straight off of a DVD player.
Testing will continue, and the next step is building the Windows Media Encoder. If everything goes right, I won't have to use Windows Media Encoder or Windows.
One can hope.