Hi @awelsh,
I might have a different suggestion.
You can try to fit a model, use the Profiler and open the Simulator.
From here, specify Uniform (or other distributions types) over your experimental space, any noise added to the response and the number of simulated points, and click on "Make Table" :

You will then have a new JMP datatable, and on this table there is one column "Obj" linked to the desirability of your response. You can then sort the simulated points by this column and highlight/export the best points :

You can also use the scripts added to the datatable to visualize the points of interest :

Hope this answer will help you,
Victor GUILLER
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)