Although I do absolutely believe in God and value my spiritual life, frankly sometimes I think that the "turning it over to one's HP" can be viewed, and used effectively, as a mental trick to help you let go of things. It's like having a mantra to help you meditate: the OM phrase or whatever doesn't have any function except to give your restless mind a little toy to play with, because getting your consciousness to be quiet and hold absolutely still is much more difficult than repeating a phrase over and over... but the result is much the same.
Instead of turning your problems over to God/HP/the Great Cosmic Muffin, imagine taking them to a huge cliff at the edge of the universe, and pitching them over the edge. The point is to teach yourself how to be less burdened by them.
Some alanon groups were too overtly Christian for me too-- I go to a pretty secular one these days.