Well, with a few minutes of searching today, I discovered a way to do this. Vim has the ability to have certain commands executed based on the file name pattern; that's how it does syntax coloring, for instance. It turns out that this pattern matching is flexible enough to handle my case. I added this to my global _vimrc:
autocmd BufRead,BufNewFile c:/dev/client1/* so /dev/client1/_vimrc
autocmd BufRead,BufNewFile c:/dev/client2/* so /dev/client2/_vimrc
autocmd BufRead,BufNewFile c:/dev/client3/* so /dev/client3/_vimrc
Works as pretty as you please.