That's a bummer man. Not having heard the tracks I don't know how bad the distortion is but even though the control room was a zoo I am sure and sounded like crap, if you weren't hearing it coming out the speakers while you were tracking it, chances are 99% of the people listening to it aren't going to be noticing a few clips.
Like you say, Layzie knocks it out and it's killer and all in all the only thing that would mess it up at mixdown is if you mix the vocals too quiet.... A little distortion here and there can be cool, like someone else said maybe you can fuzz the whole thing out a LITTLE (i.e. run it through some outboard gear or something to give it a little roundness overall) and let the performance do the talking.
Also if YOUR vocals sound all nice and crystal clear and his sound fuzzy and weird you may have some problems down the road so if I was you (I can't rap a present to save my life but..) I would take liberties with my own vocal sound distortion wise (I'm talking "slight" THD, not Boss Heavy Metal Pedal type distortion) that would make it sound like I was going for an over-the-top type of sound and that his came out a little cleaner than mine did...
I would forget the whole "having Layzie Bone re-cut his vocals" idea altogether... Not to be a downer, but if I am right in assuming that you hired him for a guest spot on your track, it's a safe bet that he's done with it and the only way to get him to do it again would be to re-hire him to do it and at that point you might as well have him do a different song. Again, if he wasn't complaining that it sounded like crap when it played back out of the speakers as he finished it up, I wouldn't worry about it too much, it's the heat of the moment and you have it, and I am sure it's awesome...
Here's hoping I get another 2 months with Bone this year, I am in my kitchen with my first gold record of "Strength and Loyalty" as I write this
Good luck man, don't let the little technical details get you down, it's all about the music after all isn't it... Oh, I forgot, this isn't "music slutz" he he