Wood Bowl Smoothing

I got a beautiful old French clamp at a yard sale for 10 bucks and Jerry rigged it to my workbench (it's supposed to be plumb but doesn't matter much for my purpose. Unlike the now ubiquitous parallel jaw bench vice, this has a pinned connection at bottom allowing one to clamp oblong objects as one would do with a Jorgenson clamp. Using a razor sharp draw knife to smooth (that's paint on my chair, not blood); along the grain is easy; across the end grains is not so easy.