Question about projected dxf files

Hello, everyone. I’m using Shapr3d for about 2 years now, and i was wondering about a feature, that i’d need quite a lot. If i project an dxf to a rounded object like a vase, it deforms on the curve. Is there a way to make it flat again? for instance, i made an urn with a cross on it. And the cross deforms on the curves. I offset face out of the object, cut the urn in half, rotate the back half to front and subtract the front half of the urn, so i’m left with the curved cross. Is there a way to make that cross flat with the same dimensions? i want to print it flat and glue it in with different colour, so i get a nice effect. Is that even possible in any software? Thank you for your help or any contribution to resolving my problem.

Have you tried selecting the lines on the vase and projecting them back to a construction plane?

Well, kind of. I tried to project that cross, that was curved from the urn and isolated, to a flat surface, but it’s not the same. It doesn’t work as it should. It’s not a plain cross, it’s quite complex.

I’m open to more suggestions.