So, I called a carpet cleaning company to make an appointment to come clean the carpet in the mini man-cave and found out they also do tile and grout cleaning. Well, I was all over that like white on rice!
Oh...and we discovered the grout had never been sealed in the first place, making it crazy susceptible to stains. Shooter promptly sealed it when it was dry. Now...we just have to get those pups to quit peeing in there! (but honestly I'd rather them pee in there than on my laminates where they can do more damage)