CL82 - good questions...and I can only speculate as what I have read in the public space re: these deals does not to get into that kind of granularity. With that in mind, here is my speculation:
The GORs, IMO, remove the financial incentive for a team to switch conferences in the first place as opposed to physically stopping a team from moving.
Let's use your example: Team X moves from Conference A to Conference B - and network 1 covers both Conferences. I don't believe either Conference A or Conference B have "sold" "ownership" of their media rights to the network; rather, they have signed media deals with the network in which they place their "owned rights" to the network in exchange for certain performance considerations (fees). I believe, actual ownership, however, stays with the Conferences. In this scenario, if Team X moves to Conference B and network 1 increases the media deal for Conference B; as the "owners" of the media rights for Team X, Conference A would be entitled to whatever revenues are generated by Team X in the new Conference. How Conference A divides those revenues would presumably be in accord with its bylaws, which could mean that each team in Conference A gets a bump as Team X is bringing in more revenues under the new media rights deal for Conference B. The question I have is what is the obligation to Team X from Conference A? On this, I just don't know; but I would presume/speculate that Team X would continue to get paid under the Conference A formula - which, as I speculated earlier, removes the financial incentive to leave in the first place.
Again, let me stress that this is just my opinion/speculation. However, it seems to make sense as these GORs obviously have some "bite"; or they would not have been created in the first place. I am sure there is more info out there - especially as to how they work in the Entertainment industry - where I have heard they are more prevalent.
Just my 2 cents.