I have found that these hook wrenches may need to apply a lot of force on those notches so fit is crucial. I see that on the Hozan you got, the tooth on the hook is not square to the edge of the notch. This may/probably will slip out and bugger the ring, even the tool. However, the wrench really only needs two contact points: the hook/notch point and one other for leverage. I've made a spacer when needed that goes between the wrench and the ring (say down at the 8:00 position on your photo). Size the spacer (a bit of hard wood, a nut, a bolt) to angle the wrench out so the hook enters the notch square to the edge of the notch. I held my hardwood spacer to the wrench with masking tape. Worked nicely.

This strategy also means that hook wrench can be used on other sized lock rings - appropriate spacer for each.