Good luck.
If you dig the music, cool. If I had to listen to those songs more than once to mix, I think I'd opt to end it all and save myself the agony.
But really, I don't think anyone (that I noticed) said to tell them to play to click or gtfo. Just try to convince them its best for the final product. Again, you don't have to edit it to machine levels, but having a guide to keep things cohesive is a good idea imo and it definitely helps for punch ins and overdubs.