After reading this survey of methods for controlling FDR and considering my problem at hand (https://genomebiology.biomedcentral.com/articles/10.1186/s13059-019-1716-1), IHW seems like a good choice.
In order for IHW to perform well, it needs an "informative covariate which is independent of the p-value under the null hypothesis". In other words, something meaningful that isn't related to the p-value when the null hypothesis is true. My understanding is based on this: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4930141/.
In my case, my hypotheses correspond to tests for association on 2x2 contingency tables. It seems like maybe the count of positives (sum of the first row in each contingency table) might be a good choice? I'll of course make the diagnostic plots to see if the choice makes sense. But I still don't have a good grasp of what the covariate is supposed to represent and how to choose one, even after looking at some examples.
Can anyone help with my understanding?