When reviewing the question and answers it looks to me they are not belonging to eacht other.
What I extract is:
The File-associations in Windows are a way to tell wich program to start for that file. That is working well.
The answer getting back is about correcting those file-associations.
The question/issue is that clicking on file in Windows will open up a new program every time. That is quit normal behavior (try word or others).
The file association can tell wich program to start, it does not know and cannot know (random pid) whether a program is already running.
Only with a smart inter-process communication set up this can be solved. Question: Is JMP having this option?
Starting open a file from within a running program (JMP or ohters) does know itself the own procecess id, pid).
In that approach very easy to open up multiple files by himself.
Solution:
Instead of double clicking the easiest approach could be drag-drop the file to a running JMP process.