Sorry, but on what planet is UConn too good for a H/H with URI? They're a top 25 team this year, have been top 100 the last few years and seem to be set up to succeed for the long-term. It's not the sexiest matchup, but UConn doesn't need 100 P5 home-and-homes. They need consistent solid RPI games and just by being competitive in the A-10, URI provides exactly that.
UConn has played at mids before too, in case you forgot. They've played at Buffalo, at UMass, at Rice, and at UCF (Big East days). That's just off the top of my head. Being in the AAC does not mean UConn needs to kill itself with its schedule, it means it needs to schedule wisely. Give me a game at URI over a home guarantee any day.
There are a limited number of H/H series UConn plays each year. URI does not warrant one. It's that simple. UConn needs both a team with likely a decent RPI and one that will garner some national press/TV coverage. URI may provide the former but doesn't bring much in terms of the latter.
If UConn successfully joins a P5 conference I think you might see some H/H against some of the other regional teams (PC/URI/UMass/etc.) that just aren't reliably good enough to get one now. If UConn fails to enter a P5 conference those games might come about but the likelihood drops significantly.