I'd use the simplest method to power up weapons in order to get above Damage Thresholds. All dice of damage (manufactured or natural) for weapons are doubled. Short swords do 2d6, Longswords do 2d8, Greatswords do 2d12, and converting
Monster Manual monsters is easy (Hill Giants do greatclub 4d8+10 or rock 4d6+7).
PS: I know that greatswords start with 2d6 damage but I think it's too good and it isn't elegant because all other sword/axe comparisons use the same damage die but different critical hit stats except Greatsword (2d6) versus Greataxe (1d12).