TomAtoes, TOMaTOES....in my definition, it would be a hip quiver. Never even heard of a "side" quiver until recently....doesn't mean they didn't exist decades ago, I guess. But I understand where you are coming from, Rob....not sure the original post was so definitive though.
I will say that the closest thing to the absorkee...the one it was modeled after most in it's design and the way it "rides" is the Idaho Side Quiver...I think it's called, which has been around for decades. So there you have it! And you are right, in that the fletches ride straight back...that was the point. That was also the point to the quiver caddy "angle", that is used with the absorkee. Either way....it works for me.
For the range...a "hip" quiver, like Rob describes would work fine.