The very dirty solution I just found is to do exactly what you described, declare your path as Environment=PATH=/run/current-system/sw/bin/ or /home/your_user/.nix-profile/bin/.
Very weird to me that it doesn’t work as it does with system services.
Edit:
The solution was right in front of my eyes the whole time:
I had read that thread before but didn’t quite understand that this is exactly what we were looking for.