Do you mean that you want to only apply to top programs? I don't think that would be wise for any student, no matter the strength of application. Are there lower ranked schools that have faculty who match your interests? I think you should definitely ask yourself, for lack of a better way of putting it, how badly do you want a Ph.D.?
I am going to be very honest here and I hope this doesn't sound rude: there is a fine line between discussing "extenuating circumstances" and getting into a competition in suffering. I would advise you to be cautious about depicting your circumstance, tragic as it may have been, as the type that is insurmountable. If for no other reason, you cannot be certain who else is in your applicant pool whose application is being read alongside your own.
There is an excellent article floating around about kisses of death in the graduate school application. You may want to check it out. While no program can discriminate against you for mental health issues...well...yeah, I wouldn't put it in my application.
It is enough to simply address the issue, but, in my experience, it is best to place the overwhelming focus on your background and accomplishments.
The recommendations will be a key point for you. You ideally need someone who has supervised many graduate students and who can address your ability and commitment to become a professional scholar.
I wouldn't pay attention to the publication advice, though. In fact, I find there is a disconnect between the amount of people giving this advice and the amount of people actually having publications before entering graduate school.
Also, if you got a 790Q on the GRE, I wouldn't take it again. I don't think there is a statistically significant difference between a 790 and 800, is there?
I was.