I think you need to show this to a number of contractors and have them voice their opinions.

Thank you for the advice. We do need to hire a contractor, I think.

I recently purchased a new home with virtually the same situation. There's a flagstone patio over a screened porch. The porch has pine tongue in groove ceiling so I can't see where the water is really coming from. To the points made earlier, I would have assumed the water proofing was below the flagstone but I can't see anything there either. What did you learn in your situation?