I am looking to dry in below a screened porch that is essentially deck a with a roof. I'd like a watertight, usable room below, and I 'd like to have an upgraded floor covering for the porch, like tile or stamped concrete. Any suggestions on how to proceed?

Id say underdecking is what you need , you can look at it on there web site, underdecking.com, or Lowe's or home depot sale it, on special order.
Even though you have a roof over the porch there will still be blowing rain that comes in that will have to go somewhere, underdecking will take care of that , however if you put sometype of flooring over the decking boards this system will not work, now I may of misuderstood you if the stamped concrete will be on the bottom, if so underdeck is the way to go.