Asking for a letter of recommendation from a professor who's witnessed my breakdown
I've had students ask me for letters with some wording along the lines of "if you feel you can write me a strong letter."  From what you've said, it makes sense asking him for a letter, but you might consider this approach: 

First let him know that you're interested in this program and see what he thinks about it.  If he's very supportive of the idea, then you should have nothing to worry about asking for a letter.  If he's not, you could ask for other suggestions.  (And even if he thinks it's a good idea, he may suggest some other other opportunities as well.)