I think the OSC’s reproducibility project is much more of what you’re looking for, if you’re worried that Many Labs is selecting only for a specific type of effect.
They focus on selecting studies quasi-randomly and use a variety of reproducibility measures (confidence interval, p-value, effect size magnitude + direction, subjective assessment). They find that around 30-50% of effects replicate, depending on the criteria used. They looked at 100 studies, in total.
I don’t know enough about the biomedical field, but a brief search on the web yields the following links, which might be useful?
Science Forum: The Brazilian Reproducibility Initiative which aims to reproduce 60-100 Brazilian studies, results due in 2021.
Section 2 of this symposium report from 2015 which collects some studies (including the OSC one I list above)
This page references some studies from around early 2010-2011 which find base rates of ~10% for replicating oncology-related stuff.