In that case, it seems to me the prior is at odds with your own observations. If I take it correctly, the patients from the study did not show such large bleeding rates. Then again, a study is only a limited sample. Had they included more patients, chances are, you’d see a much broader distribution for \eta.
Maybe patients cluster into low- and high-frequency bleeders and you could use a mixture model, i.e. different priors for each category?