That’s a great variant. I’ll have to try that with my group.
One that we’ve been pretty happy with for playing a shorter game (we play with several expansions, so a full game can be long) is to play to a set point limit. As soon as somebody reaches x points, the game ends and you count up all the points on the board. It makes for interesting games because it changes the relative worth of points on the board and points on the scorecard.