Working on a file in two git branches at one time

I have a file in two different branches of a project that is so drastically different (hundreds upon hundreds of changes) that merging was becoming unreasonable. I’ll call that file CONVOLUTED.module.
I wanted to go old-school and compare the files side by side. Cutting and pasting changes with regular commits so I could test the incremental changes as I manually merged the files.
I figured there are several options to do this.