What type system fits the subclass of λ-terms that can be reduced optimally?
I think that the type system you want is elementary affine logic with fixpoints.

A distinctive feature (actually, the distinctive feature) of light logics, including elementary linear/affine logic, is that types do not ensure termination: unlike usual logical system, cut-elimination follows from a structural property of proofs (namely, stratification), the logical complexity of formulas does not play any role.  Types in EAL only give you well-formedness properties (like progress, i.e., normalization doesn't get stuck; or the fact that the normal form will have a certain shape).

The fact that cut-elimination holds regardless of types means that you can add arbitrary type fixpoints to EAL and you still get normalization with the same complexity bounds (elementary), because you still have stratification.  With type fixpoints, Scott numerals get the following type:

$$\mu \beta.\forall \alpha.(\beta\multimap\alpha)\multimap\alpha\multimap\alpha$$

A paper that uses EAL+type fixpoints explicitly is

Patrick Baillot. On the expressivity of elementary linear logic: Characterizing Ptime and an exponential time hierarchy.
Information and Computation 241: 3-31, 2015. 

You will find formal definitions there.  However, I am afraid that no implementation exists.