pedestrian: Ok, update: I found this site where you can create an account and play:
http://www.playok.com/en/makruk/

I played a couple of quick games. It works this way: When all pawns are gone or promoted, you're presented with the option to start counting (I don't know if this applies to both players. I was behind in material). When one player is down to a bare king, the counting starts over - but this time it's automated.