Hello @ComplexNerd,
You can right-click on any table of the analysis report, and select "Make into Data Table" / "Make Combined Data Table" (if you have several responses) to create a JMP table with the values you want (example here with the Summary of Fit):

I frequently use this functionality to create visualizations about terms included in the model and their relative importance/size with the table generated (here with the "Parameter Estimates" table) and Graph Builder (with or without the intercept using Local Data Filter):

It can also help visualize different models performances and may help models comparisons and selection.
Hope this answer will help you,
Victor GUILLER
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)