is there a chance there's one that works similarly but like...for shippy fic also?

there's femslash_minis which is a Buffyverse femslash exchange, which is tons of fun.
there's also a Bellamy/Raven exchange for the 100 run over on tumblr

but I don't know of any small multi-fandom ship exchange that runs on a monthly schedule like multi_genfic does, unfortunately. Yuletide, Not Prime Time, and Rare Pair are all annual.

I bet if you organized a community, or found someone else willing to mod, that people would be interested in doing it, though.