I'm usually a "restarter" too. I go through phases where I try to play all games straight through, but they don't last. I noted the same problem as OP when trying to determine how many games I've played. On modern Sterns, I found a way to get # games played.

There are audits that give number of games played per a time range. This data seems to be generated only by COMPLETE games. For instance, at one time I noted that the sum of these "timed" games was 1637 games, compared to 3426 "total plays", which I assume includes the restarts.

I was calculating average game time, and dumped audits and imported to a spreadsheet, screenshot copied below. This might give you an idea as to how to determine total complete games (just ignore right 4 columns).

beatles spreadsheet (resized).png

Audits menus -> dump

and on my machines it asks you to insert a USB drive. There are USB jacks in the back box (can't remember which one works). Machine will dump text file to USB drive.

IMG_7106 (resized).jpg