How do I go about explaining an unproductive 2-yr gap without destroying my chances?

I don’t think you should tread this topic. Don’t even dedicate a line or two.

Discussing personal issues of this nature is always extremely risky. It’s simply not worth potentially crippling your application for the sake of transparency.

Since you’re not explicitly asked to talk about those two years, then you’re under no obligation to explain. As @lookingforward said, capitalize on your current achievements.