What I found when I looked at this, is that JMP enables/disables the rt click for clicking in the box, not rt clicking on a selection. So, if you rt click on the word "Optional" in the box, and the Menues Enable(1) has been specified, you will see the selection of "Paste". If Menues Enabled(0) has been specified, you don't see anything when you rt click on the word "Optional"
I think your work around with the subcontext men is what you will have to live with.
I am not aware of any option to turn off the rt mouse click options for the specific columns.