You asked which DVR. It’s NextPVR. It is free and I use a tool to create good quality XMLTV for the EPG.
Regarding the overlap, which it can do. With NextPVR, you can record programs from all the subchannels of a given frequency using the same tuner. For example, CBS and the CW share frequencies/transmission tower in Buffalo. Same physical channel, different SIDs. I can record programs from both of those channels at the same time using only one tuner. You don’t need to do anything to make that happen, the DVR logic just figures that out and does it. This, of course, increases the number of programs you can record at a time with the number of tuners you have.
Pretty sure Plex can’t do that either - given that they can’t even overlap the same channel. Given that Plex DVR is a paid DVR, you’d hope that it could do the things that a freebie can do – but it just doesn’t.