I'm riding a 1989 Trek 1400, which I like a lot--it's light with a "bonded" aluminum frame and sleek with internal cable routing. It fits me well, but it would be cool to change a couple of things: I wouldn't mind a least one more lower gear. It's got 14 speeds, some of which I never use. I don't like to be going through many gears, but a lower one would be nice for spinning on bigger hills.
I've got downtube shifters too, which I actually like and have become used to. But if I get aerobars, it would be great to put some shifters up top. I think this kind of change would end up costing more than the bike is worth. At least enough so that it may be worth looking at newer bikes. In that case, the Trek could be a great fixed gear project.
Ultimately, I'd like to change the engine out too. Current one goes a little slow, needs to pick up mph! At least it enjoys the ride
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If you do stick with the bike, I'd say one way of making it more raceworthy is to get used to using those downtube shifters. I think you need to anticipate shifts some more with them and get used to reaching down at speed. I think upgrading to bar end shifters could be an option too?