I had some more time (actually started this the other day). Starting with 2014-2015 when UConn left for Hockey East and not including 17-18 because I don't have enough information on the other teams yet, we've played Bentley, Niagara and Robert Morris 10 times each - 2 seasons with 4 games, 1 season with 2 games (counting regular season only, of course). We've played Army 6 times (2 per season). We've played the other teams 8 times each.
Here is a list of the teams we played 4 times each year:
2014-2015: Holy Cross, Niagara, Robert Morris, Sacred Heart
2015-2016: AIC, Bentley, Mercyhurst, Niagara
2016-2017: Air Force, Bentley, Canisius, Robert Morris
Here are the teams each time has played 10 times (and 6 times) in the regular season, which shows how often they get teams 4 times/year.
Air Force - Canisius, Niagara, Robert Morris (Mercyhurst 6 times)
AIC - Army, Canisius, Holy Cross, Niagara (Sacred Heart and Mercyhurst 6 each)
Army - AIC, Bentley, Canisius, Mercyhurst (Niagara and RIT 6x)
Bentley - Army, Mercyhurst, RIT, Sacred Heart (Canisius and Niagara 6x)
Canisius - Air Force, AIC, Army (Bentley 6x)
Holy Cross - AIC, Niagara, Sacred Heart (Robert Morris)
Mercyhust - Army, Bentley, Niagara, Sacred Heart (Air Force, AIC)
Niagara - Air Force, AIC, Holy Cross, Mercyhurst, RIT (Army, Bentley, Sacred Heart)
RIT - Bentley, Niagara, Robert Morris (Army)
Robert Morris - Air Force, RIT, Sacred Heart (Holy Cross)
Sacred Heart - Bentley, Holy Cross, Mercyhurst, Robert Morris (AIC, Niagara)
It's interesting to me that Niagara is the most "unbalanced", with 5 teams they have played 10 times each, and 3 teams they have only played 6 times. Everyone else is 4x10 and 2x6, or 3x10 and 1x6.