Fwiw, I wouldn't be going with a 12T sprocket, as the front chain slipper might be eaten even faster than usual.
I ran 13-48 up until recently (retired both bike and me from work, and need more travel ability, so now 14-48), and I agree that for some horrible terrain 1st gear isn't low enough.
+1 for the 13-51. Probably should've gone there myself...