Thanks for confirming what I suspected, Luker.
Yes, I am planning on riding this bike. I cleaned up what I could yesterday, and took it out on a test ride. The bike rides really well, and the shifters work perfectly. Apart from the wheels, I am quite happy with it. It is really comfortable, especially with the nice broken-in Brooks B17 on it.
I'll spend the next few days fixing it up. I'll look out on Ebay for a set of replacement wheels. If any of you see something that looks interesting on there, please alert me about it.