It's hard enough to get a ring off all by itself when you have a little experience chasing rings, so getting a perfect ring when you haven't had much experience is mighty challenging. NOT saying you can't, but don't work yourself into a lather over it.
If you take off a little of the next ring without biting into the early wood below it, you should be fine. You just want to use more finesse when chasing rings than when you are hogging off sapwood like osage. Any time you feel like you are making no progress, go get a large bucket, fill approximately 1/3 full of ice, add a dash of salt, and fill with cold water. Submerge your head until the feeling subsides. Towel off and return to the stave and go back to finesse work. Someone on here used to say, "Softly, softly, catchee monkey". Good advise.