Having difficulty replicating Gertler, Sala Trigari (2008)'s IRFs

Something like this is very hard to debug. I would recommend checking all equations again, including the timing. Make use of Dynare’s LaTeX-capabilities for this. Do the same for the parameters. If the difference still persists, either the equations in the Appendix are wrong or the original authors did a mistake. Usually, I recommend working the nonlinear model, because it makes it easier to check the equations and the correctness/consistency of the steady states.