How to explain a recent bad semester to graduate school admissions?
If you explain as eloquently as you have here what happened, I cannot imagine a semester hurting you.

What impresses admission officers is when they see people who have a passion about themselves, and express
intellectual curiosity, but at the same time, are willing to be vulnerable.

If you explain what happened on your statement of purpose, just as you have here, that will go along way with admissions. 

My answer is that one semester of subpar grades will not hurt you.