The two-cardinals transfer property and resurrection of supercompactness

We show that the transfer property (N₁, N₀) → (λ⁺, λ) for singular λ does not imply (even) the existence of a non-reflecting stationary subset of λ⁺ The result assumes the consistency of ZFC with the existence of infinitely many supercompact cardinals. We employ a technique of "resurrection of supercompactness". Our forcing extension destroys the supercompactness of some cardinals; to show that in the extended model they still carry some of their compactness properties (such as reflection of stationary sets), we show that their supercompactness can be resurrected via a tame forcing extension.