Rochabian,
From looking at the way the data.db3 file is constructed, I have a feeling the Most Played list is generated based on gameplay statistics that are recorded there. By reinstalling GameEx, you may have reset the data to zero. It's possible that the reinstall fixed it, but you may not have played enough.
Try launching a game at least 6 times and leave at least one running for 30 minutes. Then see if the list starts populating. If not, please post the data.db3 file so I can check it over here.
Alternately, you could try the attached data.db3 file I tinkered with while I was testing. It only contains data for a few Mame games. Just rename your current data.db3 so it is not overwritten and then rename the test file. The only thing is that I don't actually know how the Most Played functionality works, so there may be other files that come into play.
Also, I would not worry about the LastList.txt file. Yours is very similar to mine. There are no game names listed there.
DATA_test.db3