I was able to make it work! After installing JMP15, everything worked fine. On uninstalling previous versions of JMP, when opening a jmp table from file explorer, windows would ask to select an app to open this file. When you do this through this windows prompt, it will cause a new occurence of JMP to open each time you open a jmp data table from file explorer. Resetting file associations didn't help, uninstalling/reinstalling didn't help - windows seemed to remember this choice, no matter what.
However, if right after the JMP 15 install and after the uninstall of the previous version you go to JMP 15/preferences/windows specific, and then reset the file associations there, this issue does not occur, and clicking on a JMP table in file explorer opens just the data table (with JMP already open), and not a new occurence in JMP. We were able to try this out as we had multiple coworkers installing 15 and uninstalling older versions.
SInce I had already done the windows propmted file association, I needed to go into the windows registry. We emptied the Computer\HKEY_CLASSES_ROOT\JMP.Document\shell\open\command default value, and backed out, then went to JMP and reset the associations under preferences. It worked! The same value appeared in the registry again, but it worked. I can now, with JMP open, open up JMP data tables again from file explorer in the JMP version that is open without having multiple occurences of JMP open up. Just sharing in case someone runs into this, as it really bugged me, and took me a good portion of the day (and willing coworkers that didn't mind me doing stuff on their computers) to figure this out.