Technique question - A cove in a cross-grain/bowl turning

I know that the basic rule is to cut 'downhill', with the grain, but aren't sure in the case of a cove in the outside of a cylindrical cross-grain turning. To cut with the grain, the cut needs to be started in the middle of the cove, tapering off shallower toward each side, but this doesn't feel right.



It feels more 'right' if I do it like a spindle turning, working from each edge of the cove toward the centre.



Any thoughts/advice appreciated.



(I could use my carbide tools and work either way, but want to use a bowl gouge for more practice.)