Hi @StarfruitBob - can you share the version of JMP and platforms that you are using?
Retaining reference lines can be more challenging with Column Switcher, because the script usually identifies the axis by the column name, but that should not be a problem for the Data Filter, and as you indicated the script still shows the reference lines.
If you double-click on the axis after the reference lines disappear, are they still shown in the axis dialog? If so, you might want to right-click in the graph frame > Customize to check the ordering of the frame contents. The ordering should also be retained as part of the script, but if it is not then the data elements may be drawing over the reference lines: