Seems like a good plan. The crank may be quite heavy, but I'm not sure how much more than others. The other components won't be a ton heavier than their lighter counterparts, but it all adds up. I would think that the bulk of the heaviness is in the frame, but I'm no weight expert.
As far as tires, yours may be fine, but IMHO, tires can really transform a bike. All the contact points, where you contact the bike, and where the bike contacts the road, can make a huge difference. I had tires on order before I received my latest bike. But that was a cyclocross bike, with cyclocross tires. As I'm using it as my road bike, it was a no-brainer.
I guess what I'm getting at is that the bike will never be really light, it just isn't made that way. However, there is no reason why you cannot make it more comfortable. Also, the weight isn't really too big a thing. Hell, I'll bet my Jake weighs in the high twenties, though I've never checked. Doing small things to make it work out for now, and saving for whatever it is that you want, seems like a great idea.