If I were you, I would choose to just be honest. The reality is that a professor has let you down and it is not your fault. I really doubt the new recommender would read that far into it so as to think you are implying she is some last choice. Professors interact with recommendations from a far less grand scale -- many of them write them every season in significant number and while they care, it's less massive than from the applicant perspective -- and they are aware students need to make sometimes arbitrary decisions around whom they ask, and hopefully she sympathizes with your bind. I'd say something along the lines of:
"In the interest of being forthcoming, I had a professor agree in MONTH to write this letter who is now entirely unreachable and so I am now a bit stuck. Typically I would never ask for a recommendation on such short notice, and I so apologize for this, but it is looking like my only choice. I would really value a recommendation from you for x, y reasons, and if you are able to swing it, it would mean the world to me. If however for any reason you are unable to, I completely understand."
stressedout4real got a reaction from crunchyfallleaves in Do I let the back up know they're the back up?