I'm so happy we reached the point where I can finally start varnishing! Yay!
Obviously, it would have been nice if I hadn't messed it up and added two weeks of sanding to the process, but I'm happy I finally got there in the end. Let this serve as a cautionary tale for anyone else who decides to follow in our footsteps. Be sure to test your stain on scraps. And thoroughly mix the stain beforehand.