Glue bitumen shingles onto EPDM membrane

Hello,
I have built a small garden house out of WPC. Since I cannot use nails or screws on the WPC decking on the roof, I have applied an EPDM membrane with the appropriate contact adhesive. This makes the roof completely waterproof. Disadvantage: visually, the whole thing looks suboptimal. Now I want to glue bitumen shingles onto the EPDM membrane. According to my information, however, I cannot use cold adhesive for this. Does anyone have a tip on which adhesive can be used in this case?

.. Since I can't use nails or screws on the WPC decking on the roof..

Why not?

Counter-battening on top and shooting leftover genuine roof tiles on Ebay Classifieds. In my opinion, it looks best. They are even on the mini chicken coop (for 6 chickens) at my parents' house.

Doesn't work, why?

Counter battens on that and shoot leftover "real" roof tiles on Ebay Kleinanzeigen.
In my opinion, it looks best. They are even on the mini chicken coop (for 6 chickens) of my parents

How do you attach the counter battens?

just ask the manufacturer of the foil what kind of adhesive they recommend. I wouldn't experiment there, otherwise you won't enjoy the foil for long.

Doesn't work, why?

Counter battens on it and shoot leftover "real" roof tiles on Ebay Classifieds.

I would damage the continuous EPDM membrane with nails/screws. Tiles won't work because of the roof load.