As promised, here is the result (of course I can't post a clip, but...)
I recorded through Roxio to capture the audio (I don't have Vegas set up to record), then took the tracks to Vegas to fix them.
I downloaded the noise reduction plugin, but since it's only a demo and I'm a cheap bastard, it clicked and beeped, so I didn't use it. Instead, I played with the eq, noisegate and compression.... BAM! Nice tracks, very low to almost inaudible hiss...
A smashing success!