First, yes, the two-year gap will be noticed, and you have to address it.
As for whether to present your real story straightforwardly, it’s a tough call, and there is no one black and white answer. It is a compelling and moving story, and you write it with conviction (even in the micro post format). The pros: Because it is differentiating and demonstrates great strength of character and maturity as well as ability to make positive things happen, it may well interest and move some adcom members and make them want to admit you all the more, if they are already favorably disposed given your basic qualifications. On the other hand, adcoms generally veer toward safety and tend to avoid taking chances, so it’s possible that adcom members, even feeling supportive of what you’ve accomplished with your recovery process, will ultimately step back and choose someone else they see as safer.
Assuming you reach your target GMAT, which would make you
qualified for the programs you mention (if you score 700+, I’d consider all those programs to be reasonable reaches of varying competitiveness), there are some options. (1) Put it all on the table in your applications. (2) Be restrained and just say that the 2-year hiatus was for personal reasons. (3) Mix it up -- do about half one way and half the other way, since you can’t really tell which will work better.