Stick with failure of SCH at a strong limit singular cardinal

Determine whether the stick principle (λ) is consistent with 2^λ>λ^+ when λ is a strong limit singular cardinal.

Background

The authors prove that the stick principle (λ) implies the negative relation λ^+↛(λ^+,(3)_{(λ)})^2. They also explain that stick is useful because it can often coexist with violations of the generalized continuum hypothesis at successors of singular cardinals.

However, the relevant consistency question remains unresolved when λ itself is strong limit and singular: the paper does not establish that the required stick principle can coexist with 2^λ>λ^+. The difficulty is connected to the fact that the guessing sets in (λ) have size λ.