So I tried opening my MPEG2-TS files with Windows 10's Movies & TV application. First time it didn't work because of missing codec. Second time it worked apparently after Movies & TV automatically acquired the necessary codec. Of the players I used (MediaPortal, Kodi, and MPC-HC), this is actually the best.
1) it automatically pauses under certain conditions where it should be paused anyway
2) instead of stopping to buffer, it keeps playing and shows some artifacts (much better, IMO, because it isn't a distraction)
3) the controls are minimalistic and functional (clearly designed for tablets which is okay in my book)
A shame it doesn't support tuning and such with the MediaPortal server like Windows Media Player of old but, to be perfectly honest, I'm fine with that. I'd rather add recordings via editing the MySQL database anyway and I only watch prerecorded stuff on my computer. It should hold me over until open software matures.