The amount of deflection via the eccentric cam action on the Salsa (just purchased another last week, and have "old" ones) is totally adequate if the seat-tube ID and OD are to specification.
What you are describing is a classic case of the seat tube ID being too large, or the seatpost OD being too small.
Remove the Salsa component- does the seatpost "rattle" around?
The Salsa clamp should slide smoothly onto the exposed seat-tube without any noticeable play with the binder all the way relaxed also. If it passes this test, then your issue is with the seat-tube ID or the post, not the Salsa component.
I have seen this many times before, some guys custom turn a shim and run a 27.2 post for instance, because the seat-tube was reamed oversize. Post diameters also vary.
Your condition is a no-go in my book, because you will be lacking a degree of support that a well fitting seatpost provides-