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 outside :thumbup:1000 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.