This has been resolved, I should post an update.
I'm still growing (18 years old) and both of these bikes have gotten small for me. They have 21" seat tubes, same wheelbase, similar trail, and similar top tube length. The only difference between the sizing of these two frames is the Fisher has more bottom bracket drop. This gives it a lower standover height, so my 5'1" mom can actually straddle it. I reinstalled the original stem and it fits her perfectly. I also replaced the Shimano rear derailleur with a more period-correct V GT Luxe.

I may end up needing to sell the Fuji anyway. Top of the seat tube to top of the saddle, measured parallel to the seatpost, is 7". I wouldn't even be able to have the saddle this high without a modern Kalloy seatpost. I'm building a 23" Fuji Sagres that will probably replace this bike.

My mom is planning to give her old bike, a Specialized Sirrus Sport, to my cousin when he's big enough. We're keeping the Fisher.