Just make it so the king must go to either e2 or e7 on or before move 5. Nice and simple, no confusion about what counts or not (what constitutes asap?), no trivial mates.
Special tournament trophies should maybe be restricted to daily/weekly/monthly official tournaments just to ensure adequate competition (off peak tournaments almost always have much lower average ratings). - and with this restriction the re-opening of the way of the berserk trophy should be in order, as fins expressed interest in going for it ;) I don't really understand the hard cap on trophies to begin with.