You're SC, but what faction are those unitless decks? Im guessing Monsters and Scoiatael.
I havent faced a SC one recently, but i faced one Big Monsters with just Old Speartip, and im guessing Woodland into Ozzrel into Speartip as last play, if i'd let him.
Well, SC has the best card for the job - pitfall trap. It will trigger only when he plays a unit, and if he really only has 1 unit as finisher, he'll either lose or tie (0-0pts), because usually they only carry tons of spells for damaging and removal units, not artefacts.