Thrasymachus,
I started riding a lot a few years ago with a heavy, old Trek 800 that I had bought in the early 90's. I eventually replaced the stock wheels with much nicer rims and hubs and thinner road tires (with a less aggressive tread pattern). That made a big difference and was a relatively in expensive upgrade.
An expensive cyclcocross bike would be nice, but you might also want to consider something middle of the road/less expensive. Trek, Giant and the other big manufacturers have nice "fitness" bikes which have light aluminum frames, decent components, and 700C wheels and these bikes would be faster than your mountain bike, good for commuting (they have eyelets for racks and stuff), and would be good general purpose bikes. You might be able to get a less expensive bike that would meet your requirements. I bought an inexpensive Hybrid after riding my mountain bike a lot and it was significantly faster than my mountain bike, yet affordable and comfortable to ride.
I would definitely test ride the bike before you bought it (or something very similar to it in the correct size). Also, try out some other bikes. I commute on a touring bike (trek 520). it has a steel frame but it is very ride-able and I go much faster on it than my mountain bike.