Context: I finished my application for the 2020-2021 Ph.D. program in population health science and epidemiology fields and currently I'm waiting for the results. I have a strong academic background with a bachelor of medicine degree, a master's degree in a top school, good grades, good GRE scores, a few published abstracts, and papers in review/submission, and a few years of working experience. After receiving more rejection letters than I expect, even from the schools that I already contacted potential advisors, I realize something went wrong: I contacted some of the professors I was in touch with during application and they told me that my recommendation letter can be improved, one program director told me one letter could improve the whole application substantially although they were not allowed to tell me the specific person. I narrow it down to two letters from my previous work at a prestigious institution ( I sent our 4 letters instead 3 since I have no idea which one could be a strong letter, a huge mistake from a post hoc perspective) and now my questions are:
I'm still waiting for the results from a few schools ( very promising if it's not the letter situation), is there any way to undo the damage? I asked the schools to retract one letter since it's additional but it seems it's highly unlikely. Anyone has done it before?
Should I send another outstanding letter ( the fifth letter ) to reduce the harm or there is nothing I can do?
I still have no idea which one of the two letters could be the bad one. I know one is going to be short and generic and only commenting on my passion from the center director since he already told me. Should this short letter be sufficient to do the damage or will another letter be the bad apple?
I sent out emails asking my recommenders regarding this situation and they haven't replied yet. I'm wondering what's kind of relationship should I maintain, just wishing our path will never cross again? Or I can require them to send me another good letter for other programs that has a later deadline if I still trust them?
I made a huge mistake of downplaying the importance of a recommendation letter and it, unfortunately, canceled off all of my work and efforts, hope others can avoid the similar rookie mistake