The band i'm just about to start mixing next week...

just tighten the kick...
create tempo markers from the snare (BD) and quantize the kick to those...that way at least the hands and feet will be in time...
doesn't sound like a lot but it helps immensely, especially on faster doublebass parts
 
It's not hard to get stuff nice and tight without a click, edit the bass and guitar to the drums that are there as much as you feel they need. If the performances are good then it should only take a few tweaks here and there to get it tight, if its loose as hell then they've not put enough work into tracking and I wouldn't bother editing much at all.
 
You could have play live, record the drums carefully
later on, Tempo map it the best you can now you have a tempo to edit to
Its way to much work but my brain is telling me that should work hahha
 
if youre not satisfied with the recordings, make them redo them.. it`s your name behind the mix and you have to decide what standard you will go for.. I wouldnt release a mix for a commercial album if I knew I could have done it better with tight materials.. :p
 
Are you going to be reamping these tracks using real amps Erik? I only ask because most stuff I've heard from you has all been ampsims...
Personally, I'd take James' (actofvengence) advice and create a custom tempo map. If they know that everything is not 100% perfectly in time, what do they honestly expect you to be able to do? There's only so much editing that one can do. At least you have the triggered drum and DI tracks which allows you much more flexibility with regards to editing, but as someone else suggested, maybe the 'live' feel might work just as well!
Congrats & best of luck BTW! :D