If your reputation was preceding you, you would likely not get interviews at all. Since you are, that's a good sign you're not blacklisted or something.
Don't worry that bad news about you is coming out during their reference checking or something. professional reference checks are usually along the lines of "Have you heard of this person?" "yes they worked here from x to y" "Great thanks"
I guess my question for you is, do you have any real concrete reason to believe that these companies know who you are before your resume reaches them? Or would find out about your breakdown during the interview process?
Does a really embarassing youtube video of your breakdown appear when they google your name or something?
If not, I'd say you're just having a run of bad luck. It happens. Take courage in the fact that you are making it all the way to the final stages of their interview process and keep trying. You'll get there.
Also I hope you're in a healthier place since your breakdown. Mental health issues suck. Take care of yourself.