What do you think the beach cruiser in inefficient? If you want a faster ride, you might think about a drop bar bike with fairly narrow tires. A lot of folks on this forum tend to ride cyclo cross type bikes... not the most aggressive ride but with room for fenders, slightly wider (and more comfortable) tires... that sort of thing.

If you like the more upright position though, the mixte looks very attractive. It's going to be a heavier bike though (hi-ten steel), with only 3 speed gearing. Linus has another model, Dover 5, with better steel and more gears.