I'm by no means an expert, but as they say, "its all in the wrist!" My technique,once mastered, makes short work of ring chasin. That havin been said, I also aggree that this is not a race. But let's face it we all like to see results and my experience (30or 40 osage bows) is that this is a part of the process one can get through quickly, and then spend time on the details.
I like to "open" a couple of rings on one end or the other. _sually go down 2-3 rings out to 6 or 8 inches. At this point I stand the stave up and lean it against my work bench or the crook of a tree, whatevers handy. Then take your drawknife, bevel side down, and start "peeling" the wood under the bottom ring that you have exposed. I have rarely had any trouble with my drawknife cutting down to the next ring, but this is a feel thing. You will soon start to see and feel the difference between the rings and the early growth. If that line doesn't stand out you can use a scraper (or drawknife on edge) to scrape the back till the lin stands out a little more, then continue to peel up the ring. The drawknife is designed for you to use it as a lever to pop the wood up if you feel that you have a pretty big bite. This will help you to keep from going to deep. If you get a chance to see someone do this it become obvious how easy and efficient this is for chasin rings
Hope this helps.