Though I do think BYU is going to hurt itself in negotiations, as they've basically already stated they are committed to staying with ESPN.
In terms of BYU's contract, they are "underpaid" from what we know of the TV contract; BYU wanted exposure and not money when they went Independent (and it is likely still the goal now). Because BYU has had solid ratings (not claiming they've been great, but they've matched expectations) and ESPN has been underpaying, and likely can keep underpaying, I don't think BYU will have any issues -- they likely will even get a raise in the next contract.
The trick with BYU is that they are good "filler," as they can fit BYU games on Thurs or Fri, and any time slot on Saturday, and still make money on BYU's contract. Live content has always been ESPN's bread and butter, so they want any live content that will make them money; especially now.