Cross grain inlay
 

I've built an 18" Lazy Susan to be used on an outdoor table. It is made of Ipe and I think it looks a little plain. I'd like to steam bend and inlay a 3/8" X 3/8" piece of contrasting wood around the surface, about 1" in from the edge to dress it up. Does anyone have any experience doing something like this where some of the inlay will cause a cross-grain situation? I'm concerned that the cross-grain will prevent the Ipe from expanding and contracting in the weather and cause it to warp.
Thanks for any help!

Tom