Turns out that the perturbation order that I worked on is purely dissipative and that all that work was pointless lmao.
Update: Turns out that I was just sloppy and forgot to include transition rates in the final step of my calculation. Seems like I can proceed as usual.
I remember working as an undergrad assistant to my math profs for one of their papers and them telling me that math was nice because sometimes you're allowed to publish non results like that.