ECAC hockey was similar. In the days of the four team tournament, there were (a) only two conferences anyway (the WCHA and the ECAC), and there were two "automatic bids" that went to Eastern teams. These weren't necessarily the ECAC champions, or even the top two in the standings, just the two the committee thought were the best two in the region. For example, in 1963, Harvard won the ECAC regular season (by best win%), and the league tournament, but the committee invited Boston College and Clarkson instead. A year later, Providence won both and got a bid to the tourney, but sixth place Rensselaer was the second invitee.
Non-conference slots are still the major stumbling block for this idea, although it's lessened now that HEA appears to be adopting a 22 game schedule the year UConn joins, which will give UConn 12 non-cons. Quinnipiac and Yale also play 22 games as members of the ECAC, but Yale will be limited by the more stringent Ivy League limit of 29 games (so QU will have 12 and Yale 7), and it remains to be seen what the AHA will look like in 2014-15 for Sacred Heart's schedule. QU and Yale may not also want to give up a non-con for a potential rematch (while, yes, the Beanpot does such a thing, this is no Beanpot), so this hypothetical tournament may end up having a showcase format where Quinny and Yale wouldn't play each other.