People always advocate recommenders who know you on a personal level. Frankly, I think this is kind of a crock. You want someone who knows about your intelligence and work ethic. If you've spent a lot of quality time sharing your mutual tap dancing hobby that's nice and could possibly add another dimension to the rec, but it's not necessary. Ask the professor again, tell him that you really enjoyed his class and explain your situation. (Kind of like you did in this thread). Give him an out, tell him to think about it for a few days and let you know by __day. Also, let him read your essays and explain to him why you are going to law school. Good luck!
I recently handed in a final assignment that's been due for over a year. The professor was very nice about it (I had a personal situation) and he agreed to write a recommendation for me.