Blue-Green Stains on White Travertine Steps Below Copper Roof - Any Recommendations?

Just got done building a house with a flat-seam copper roof over the front porch overhang. The front edge of the copper roof terminates directly above the second step of the staircase leading to the front porch. Unfortunately, we installed a PITA white travertine on the steps and the porch. The travertine pavers on the second step directly underneath the copper roof are developing a line of blueish-green discoloration, which I presume is from the water running off the oxidizing copper on the roof. Does anyone have a suggestion to remove the stains and prevent them from returning?

I'm considering putting a small copper gutter along the front edge of the overhang with openings on both sides to keep the runoff away from the front steps.

TIA for any advice