This, to be honest. If they broke the continuity in order to play with the Trek elements as they liked...hell, go for the big ones.
The Klingons are very famous, but in the end they are a very abstract idea...the fact that a story is 'Klingon-centered' doesn't say anything specific about its content. And they are not mutually exclusive. Say that the Borg attack the Klingons and this forces them to ask for help to the Federation...then you have a mix of STVI and First Contact. You can't go wrong with that.
I say bring on the Borg and some time-controlling device, the five captains in order to commemorate the 50th anniversary, and restore the previous temporal line.
I think it's going to be pretty difficult to renew the entire cast for a 4th movie anyway, so they may as well end things now just in case.