Inductive strength above the bounding lower bound

Determine whether, for all natural numbers n and ell with n >= 1, ell >= 1, and d_{n-1} < ell, the thin set theorem RT_{<infty,ell}^n fails to imply I Sigma_{n+1}^0 over RCA_0; that is, prove or refute RCA_0 not proving RT_{<infty,ell}^n -> I Sigma_{n+1}^0.

Background

The paper proves that, for every n, ell >= 1, the thin set theorem RT_{<infty,ell}^n implies the bounding principle B Sigma_{n+1}^0 over RCA_0. It explicitly states that it is not known whether this is the optimal lower bound for the inductive strength of the thin set theorem.

The question is restricted to ell > d_{n-1} because Cholak and Patey established that, for n >= 3 and ell < d_{n-1}, RT_{<infty,ell}^n is equivalent to ACA_0, which implies I Sigma_{n+1}^0. The cases n = 1 and n = 2 are already known to fail to imply the corresponding induction principles, leaving n >= 3 as the central unresolved case.