Probably the membrane solution is the easiest if the slabs can be lifted easily. I'd also be inclined re-lay the slabs on a deeper bed of muck so they are above the level of the slabs outside1000 guage polythene under the slabs is the only cure or at least 4inches of 10mm 30n concrete as the shed base.
I also had to worry like this when I wanted to get my shed sometimes 2 years ago until someone recommended urban sheds for me. I tried them out and to my greatest surprise they made a shed with all my full specifications for me at a very affordable price. You may want to try them out too.