Just bought a new battery with the correct cca specs, but the length is about 35mm too short.
Is there any solution here or do I need to find a battery with the exact same size?
BMW does some adaptor brackets, but I'm not sure if that's what I want.
I'm not quite sure what problem you have without seeing a photo. However, I replaced my original BMW battery a few years ago with a Bosch one that is correctly rated but turned out to be too short. I packed it with cardboard between the top of the battery and the bracket and it's been fine. I picked the Bosch instead of another BMW item because the warranty was longer.