You've got some good info here but one thing that wasn't mentioned, except by you, was to change the deck type to a sold surface.
You mentioned putting plastic down under the deck but as you correctly noted there would be holes in that when you relayed the deck.
An option is to put a solid plywood deck down and cover it with a vinyl membrane. This would give you the full drainage away from the house that you want. Not sure if you would want the look of a solid deck surface but it is easy to maintain too. Check out this website: http://www.duradek.com/vinyl-decking/
Disclaimer: I have no connection or financial interest in this product.
This a very good point, it would require a slope to the outside 1/4" per 12"