Felix,
In this case it may be best to break the whole down into manageable parts. Maybe take a line through the center and Boolean Diff.

I was able to Union the center piece to an abstract section of the spiral, which would be a good start.

Make sure that the lower inside part of the spirals moving profile is a little higher than the back end, so that the two sides are not coplanar.

Also, there is a strange "kink" in the tightest part of the spiraled sweep that may cause problems.