So, I decided to look at shelters and see if any cats caught my eye. Ginger is already front declawed and has been spayed (or neutered - whichever female cats get). Plus she has all of her shots!
Ginger was described as "obese". But...well...she seems normal to me. These shelter people didn't know Max! They told me she was really shy and would probably hide a lot at first. However, she was being fostered by a family with 4 cats, 2 other foster cats, and 2 small children - so she may have just disliked all of the noise!
She's been adjusting well, spending a lot of time in my office (her room for now!), and occasionally coming out to explore or sit with me.
Min is not a fan so far. They growl and hiss at each other, but haven't been aggressive. Min and Max never really acknowledged each other, so I don't expect Min and Ginger to be BFFs, but hopefully she stops growling soon.