(I should preface this with the fact that I only really skimmed the aamc article you linked)
I think we have a serious bias problem in medicine. However, the right answer might be to fund studies that debunk the racist claims pervading the education system, rather than relying solely on stricter policies.
It seems to me that we want individualized medicine. Discounting race, different people may respond differently to various treatments; for example, I have really long tooth roots. Therefore, we should develop tests to identify these differences and tailor treatment accordingly. I understand the fear of research that could possibly establish differences in treatment across racial lines due to historical context. However, I would tentatively suggest that if one truly believes race is an ineffective descriptor for such distinctions, then one should expect that studies would more likely aid than hinder the effort to address racial disparities in medical treatment and outcomes.