Usually, whichever team is losing the most lately talks about moving it to home-and-home. In lieu of doing that, for Smart's recruiting point, I'd work on simply changing the rule.
The rule seems like they didn't know what to do and didn't want teams with an annual neutral site game to go crazy with it and have an advantage, so they just shut it down.
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A simple, nuanced rule would take care of everything. Each school should just pick a Jacksonville-area location as a 'home site host' place, which serves as a replacement for their home stadium. There can't be any shortage of decked-out UF and UGA alumni with posh spots that could do it. Or if that's no good, have the universities purchase a site to be the hosting home-away-from-home.
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Making it home-and-home is just the most easy, direct route because the current contract ends in '23.