Okay, so thanks to RonG I'm now a member at BallerStreams..
Here's my setup:
I've got a few PCs, tablets etc, but I digged through the site and found they support Plex.. Well, SmartTV's (LG & Samsung) have a Plex app, so I was intrigued. After installing the plugin on my media server, I'm now streaming live and recorded videos in HD straight to my TV, without any effort on the PC's part (no transcoding, nothing).
So Plex is definitely the way to go so far.. I'll come back and post my review, but so far, I am amazed. LeaguePass doesn't have Plex support, and it looks like crap over broadband. So I've gotta say, I'm impressed. A few hiccups in the stream, but I followed the instructions and stopped and started the stream so it would find a nearby server (West Coast), and it looks like that worked. I'll likely take a few minutes later and narrow-down their server list, and force it to pick only servers that are geographically near me.
But overall, 10/10... The Plex support sent it way over the top for me. A totally unexpected bonus.