First, let me say that is the most interesting cherry bark I have ever seen. Not at all like ours here, but remarkably similar to birch, with the thick fibrous underbark and papery surface. The cambium, to be precise, is that thin layer of stem cells between the bark and sapwood. Your underbark has no lignin holding it firm, so it'll crumble and peck just like white punky areas in spalted pieces. Dry, it'll cut fine. I use CA to firm it when I think the bark will stay, which helps stop the peck and keeps the bark on through customer handling. Apply between the hog and smooth passes, making sure to either spritz or wait a few minutes when dealing with acid wood like cherry before turning the lathe back on.
In my experience, cutting across annual rings narrowly is prone to peck-out regardless the wood. As you start to broaden near the base of the piece, it cuts similar to cutting into the broadening figure on a heart-up piece. Not sure why this should be the case, but I rather suspect it's a case of not getting the bevel into play in the narrow gap. I overcome the worst of it by narrowing the face of the cut, so I'm not taking anything more than wire shavings on the last passes. Strictly nose work with a fingernailed grind, more bevel steady and broader cut with a forged type.
As an idea, you can see the stepped work coming in from the edges, and the wire shavings as I get ready to turn toward the bottom. Notice the twisted mess at the zero fpm point. If I had treated the bark, you'd see more of it, but this is a demo where time counts!