Maybe I miss something, what do you suggest to solve the issue?
No, I don't think you're missing anything. I think it's an interesting problem: according to your post it seems that kinematic objects have a bigger influence on the inertia than on the mass of a btSphereShape.
I don't have any solution, but I think I'd try one of the following:
1) replace the btSphereShape with a btMultiSphereShape with a single sphere inside and see if the problem persists.
2) use a very high custom friction (e.g. 10-50) through a custom material callback and see if something changes (I'm not sure, but maybe without a custom material callback the friction is clamped to 1).
3) try to modify the split impulse property of the simulation (turn it on if it's disabled).
Hope some of these ideas might be helpful