Thank you all - I think I'll try it! Are there any capacitors inside that might give me a nasty shock? That's the main thing I'm worried about. I found Rain's tute on rewiring a potted motor, which is apparently the same as for an external motor. So with that and your help, it will be done!
Pretty sure we have some electrical component cleaner. Now, to Google "armature" and see what not to saturate!