I like options one and two myself. Particularly option 1. I agree that often pvp games end before I have time to jot down information. So I think this has some real potential.
I also had another idea for an option, going off of option 1. Have the button say best of 3? And give double or nothing rewards.
Best of 3 mode would also be very useful for tournaments if put into the duel mode as well.
It would make it easier to run tournaments where there is no deck swapping between matches.
It would also be cool if at the end a text box would pop up with stats for the best of 3 results. That way we can simply copy paste to the tournament thread.