From what I am able to follow the FSTV broadcast includes 2hrs of Thom's radio show televised. It is the 2nd and 3rd hour precisely; please correct me if that is wrong. And the 1st hour then is not there. Now I do not know if Thom has some arrangement with his commercial carriers where they want to be provided exclusive material, or if this arrangement is only because of the FSTV schedule... 3hrs of Thom every day does seem like a lot.
If it is not about exclusive content. It seems like a good idea would be to rework the 3hrs to fit it into 2hrs. Since the 1st hour is missing, then it would be simple enough to work it into the live feed of the last 2hrs. Since most of the show is a combination of bumpers and the oft repeated headlines monologue. Thom could just not do the awkward sections where he tells the guest they are only going out to FSTV. And during that time plus some time borrowed from the repeated content the pertinent pieces of the 1st hour could be used as filler with just a disclaimer that it's not live for the FSTV viewers.
PS: I do record the Friday night RT programs for the "Great Minds" bits. But please if you ever have to choose between the formats, please please please stick with the radio one. RT feels like a network/24hr news channel. I don't know how else to describe it. Even with Thom there it's just tedious and not satisfying (to me)