Turn the overlap up the sides and trap it in position by placing the shed walls on top of it. You can then trim any surplus by running a hobby knife around the internal perimeter of the shed.
If the overlap is not long enough for this method you can still turn it up as far as it will go and hold it in position by making a timber frame (ideally the depth of the base) to fit round the slab. The top edge of the timber frame should then have a batten fixed to it to seal the gap between slab and frame and stop rain getting into it.This has the benefit of giving you a "finished edge" also.
It is pointless trying to stick the poly to the sides of the slab as any rain will soon find its way into the upturn and soon force it to become unstuck.
I'm afraid there is no successful method which does not involve some cost
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