There's one thing I don't understand: Why can just one player mark dead stones???
It should of course be like that:

1. One player passes
2. The other player passes too
3. The first player should be asked to mark dead stones
4. The other player should either accept the marked stones (that would finish the game) or give the chance to mark dead stones himself.
6. If the first player doesn't accept the dead stones marked by his opponent the game should continue WIT the possibility to pass again.

Ok, I know this setup could lead to a never ending game with both players not accepting the score but you could limit this sequens to maybe 2 times then the game would automatically send to the Go administrator to say who's the winner.