Hi Rusty, I haven't turned buckeye, but just to eliminate the first possible issue: are you getting the tear-out on the exterior, interior, or both? Since you're turning end grain, make sure you're actually cutting (or scraping) downhill, which is the opposite direction of a side grain bowl. On the exterior, that means top to bottom (wide to skinny) and on the interior that means base to rim. Not sure what tools you're using, but a gouge isn't going to cut smoothly going interior rim to base. Probably a scraper show on the interior, unless you pull out a ringtool.
What's the old saying? Think of wood as a pile of straws. Would you cut a straw with a pocketknife from the side or the end?
On the other side of the discussion, a side grain bowl that is wider than tall with a rim that goes beyond vertical and back inward at the top a little (like a calabash bowl) sure makes a fine popcorn bowl.