FWIW...I use an ancient draw knife that I picked up from an antique shop in town that was well used before I bought it. I have backed 20-30 staves, and I have never sharpened it. It is ridiculously dull, and I love it. It's dull enough that it will not get away from me and dig in...I have to work it good. It is "sharp" enough to get through the late wood with some elbow grease, but the dullness is such that when I hit the early wood, even if it is super thin ringed, I can easily feel the crunch. The duller the instrument, the greater the tactile feedback. There is a happy medium, but I think that happy medium is much duller than most folks would think to ever let their drawknife get.
I'm pretty sure I could go end to end with the draw knife in one go and clean it all up with a scraper at the end, but I never make it more than 4 inches before I get paranoid and go to the scraper to ensure I am still on one ring edge to edge. I use a mystic scraper which is super thick and non flexible vs the typical cabinet scrapers I see most people using, because I will often use that scraper to remove a ring of late wood and go thru the early wood to my target ring on super thin ringed staves...a typical flexible thin cabinet scraper would take forever to do that. I have not run into a stave yet that the super dull draw knife and that mystic scraper would allow me to get through without getting into the wrong ring. Just get a side to side clean spot backed on one end of the stave and go two inches of early wood crunching at a time before cleaning it up with the scraper...rinse and repeat. If you feel yourself getting impatient or in a hurry, put it down, go have a beer, and come back later.