Hm, not aware that they were mostly for screening but I had guessed from the number of effects you think you know that a fractional factorial design, perhaps with different factor settings would give sufficient information to build the next model iteration. I suspect this would mean fewer runs than a RSM, which means it saves time and it would still give you information on lack of fit. The center points appear necessary to capture the nonlinearity shown in your screenshot, and reproduction also seems beneficial. On the other hand, if you can perform experiments fast at low budget, than you are not restricted by the nr of runs. Difficult to tell without knowing more of the context.
Note, that the DoE platform in JMP allows to comparison between different designs, which may make the decision which step to take next easier.
Edit: Lack of fit in JMP help.