So I left the case in the closet for some weeks until I stumbled upon an old russian geiger counter I bought some 15 years ago on a flea market.
At that time I totally messed up the original case and never was happy with it (obviously!)
my costs for this project were:
40 $ for the geigercounter (long ago, so somehow not addable )
15 $ for the half bricked gameboy
4 $ for the rechargeable batteries
5 $ for both relays
4 rainy weekends sitting in my workshop :)