I think the sticky EPDM is the answer, but not in one piece.
A piece over the batten first, which goes up the slope say 10-15 cm, and also across the flat board by the same amount.
Then a piece that comes down the slope and overlaps the first piece. Where it gets to the batten, overlap as far as you can, probably only 3-4 cm, molding it round as best you can, getting it to stick as well as possible.
Finally, slap some of our favourite sealant, CT1, across all the joins of both pieces.
HTH