Player rating for tournaments across all installments of Heroes.

It would also be good if the system took into account the size of the map.

And what does this have to do with anything? Who said that it's easier to play on Might & Magic than on Heroes of Might and Magic, or vice versa? And the map limit is determined by far more than just its size.

minimum possible completion time

It's easy to take this into account, but how do you determine this minimum? Sometimes it's obvious after the tournament is over, and sometimes it's not.