Neither of these ideas apply...
Prior to exausting everything I could think of, the free version was not installed, and in fact had never been 'purchased' (it did not show up in my purchases list, and the button on it read 'free' instead of 'install')...
The first thing I did was a spotlight search for JPEGmini, with no results comming up.
I then went into the App Store which is when I found that it was reported as installed.
I proceeded to use the Terminal app to try and determine if a hidden flag had been set on the app in the Applciatons folder (rendering it present but invisible), but was able to confirm there was no applicable hidden item...
It was then that I 'bought' and downloade the free version, just to see if it would work. It worked as expected, and even upon deleting the app the 'INSTALLED' indicator in the App Store went back to an 'INSTALL' button...
I've since removed the free version but am still unable to install the full version...