Couldn't you get a bad study that reverses the sampling bias to get a decent picture of social distancing strategies using the two bad studies? That alone seems far more useful than knowing the IFR because its actionable information.
Or better yet, do a simple survey and ask the participants how frequently they go to the grocery store. And if you see a correlation between frequency and infection rate, then try and adjust your weights accordingly.
These bias issues are well known among survey designers. There are ways that you can try and account for them. It seems like maybe the medical community is too used to having control groups in their studies?
