The ability to synch local FM radio to NFL TV broadcast would be an awesome feature! If it’s only available on a recording versus live broadcast, I would still be thrilled with this feature. Your local broadcaster is always much more interesting and engaged than the NFL announcers on the major networks.
The Tablo can only record OTA tv signals, not radio.
If you use NFL Gamepass, you can get what you want. Open up two tabs, and have one set to “full broadcast” and the other to “listen”. “Listen” has multiple radio broadcasts of the game (home, away, SAP, Westwood one, etc), but it doesn’t have video. Just sync up the listen stream with the full broadcast stream, mute the full broadcast stream, and you can watch the game and listen to the radio at the same time.
Note, NFL Gamepass only replays games, but it is a cool site (I get it for free with my Titans season tickets).