Well, instead of having a fight at an appointed time every week, we could organize a real tournament and instead fight on dates that are appointed after the anterior battle.
As in, we organize a table where the combatants are.
Then, a battle is held, say, 00:00 GMT Sunday. The next battle's date isn't still marked. To prove it was made at that day, one of the fighters gives out a video of the fight. Not needed, but I think it's good proof.
Then, according to the availability of the next two fighters, the date for the next match is appointed.
Now, I don't know if this was already suggested, but anyway, I'll leave it here. Just in case, eheh.