To me, turn it over... simply means "Look at it from a different angle." Or, "To turn it over and look at the other side."
Example: The cat and the ball of yarn.
I can look at that as "an idea in an undisciplined mind" or, I can look at it from a different angle as... "the cat is just doing what cats do... they play with things."
I could get ticked off at the cat for making a mess... but by turning it over... and looking at the other side... how can I get ticked off by a cat doing what cats do... which is to play.
That kind of "turning it over" helps me to maintain some emotional balance rather than be disturbed by emotions such as anger and resentments.
Another example might be: "I'm not making mistakes... I'm learning." Two different sides... one I can feel good about and the other I can use as a hammer and clobber myself with it.
As far as "turning it over to HP, or God"... that's a little too abstract for me. If it means to "just accept the outcome of something, the way that it is, rather than what I demand it to be"... I can do that.
In regards to "turning my will and life over to" God, it meant that I was willing to change my mind and change my actions... for the better... and accept the results... whatever they may be.
In other words... make progress in cleaning up the messes that I had made in life, and try to make less of a mess. To pursue things like character building... It meant, that I was now willing to do the "foot work" and to "pick up the Spiritual tool kit" that had been provided to me, and for me to "go to work" with the tools... instead of handing the tools over to God, and asking Him to do my job for me.
Thanks for letting me ramble on this controversial topic!