I remember from my own time in recruit training they taught us to kneel on the affected artery while we were applying the tourniquet

This was in the original training! A step in the original classes that kind of vanished in the later trainings (from my memory at least). I think most people missed the artery when they slammed their knees into people anyway. I dunno, I didn’t ask so I don’t recall why that step kind of vanished. Probably no longer trained because it got in the way of people getting it high enough as well. I bet it would still help if performed correctly though.