Thank you so much! I just managed to get it working!!!
First of, I had all the matrix stuff right. Despite me not really understand it (I do now, I think), it was correct. I apologise for waisting your time.
Your foolproof explaination helped, because you mentioned that
anim-pose-vertex = model-space-vertex-position * offset-matrix * anim-pose-matrix
The problem was the follwing line in the shader that does the final skinning:
Output.Pos += mul( Pos, boneMatrices[boneID] );
Notice the "+=". I'm about to kill myself.
Literally weeks waisted because I forgot to check that.
Again, thanks so much. Without you mentioning what I was actually trying to compute I'd have waisted who-knows-how-much more time.