If the issue is that the grips are too bulky, would it be possible to remove the grips and wrap the bars with tape instead? On my old bike, I had grips and bar ends, and I had wrapped the bar ends with tape. I would think you could do the same with flat bars.

I've read in a few places that it's much safer to ride with your thumbs hooked around the bar, not resting along the top of it. Our good ol' opposable thumbs apparently make a big difference in bike control.