Trouble conforming SVG to curved surface for engraving

I’m trying to print an Easter egg and want to engrave a design onto the surface. The issue I’m running into is that the design I want to engrave is flat, while the egg itself has an oval/curved shape.

Because of that, I’m having trouble getting the design to conform properly to the egg so it engraves cleanly across the surface.

I tried importing the design as an SVG and using the “Use Surface” option in Bambu Studio, but I can’t seem to get it to behave the way I want.

Is there a good way to make a flat object or SVG conform to a curved surface like this for engraving? Curious how others usually approach this.