I beat 9 challenges without SoUs, Tengu's mask and Crown

You can use it to blast non-airborne enemies into chasms which instantly kills them. It'll give you significantly less XP, but can get rid of problematic enemies real fast.

Still, it's astonishing to be able to beat 9 challenges w/ so many self-imposed limitations!

Easiest way of insta killing enemies by just pushing them off cliffs. Other ways might be with the repulsive/ bouncy glyphs/ enchantments, but they're unreliable and the enemy has to be at melee distance of you. You can make them reliable with a Ring of Arcana too. The last way of insta killing enemies easily might be with a grim weapon and an upgraded Ring of Arcana. I don't know what level the RoA has to be to reliably kill execute enemies, tho. Maybe +6, which you can do without using SoU, but I don't know.