Having converted an old Trek 400 for way too much money, I'm going to go out on a limb and say you should convert. Are the wheels really toast? If you can salvage the front wheel, you're looking at buying a brake, lever, BB, crankset, and fixed rear wheel. You can do this for $100, if crafty on EBay. OR you can talk a friend out of some parts he'll never use in his parts bin.
Or you could buy the Redline for $300, I think. But the conversion will be more fun.