What are options to increase difficulty?
Aside from the ways you already mentioned, you could increase received damage (actually, reduce your defence) by using clutch rings. They also occupy ring slots:
- Dark Clutch Ring
- Fire Clutch Ring
- Lightning Clutch Ring
- Sorcery Clutch Ring
You already named almost every option. Increasing NG, and joining Champions. The only other thing I can think of, is constantly using knuckles, to increase your invasion chance.