I only mention the laser-cutter because I use one everyday in my workshop. Looking at your designs, I'd say they take at most 20-30 seconds each (for 1/8" or 3mm acrylic) on a machine like mine.
All laser software is different, but most of them can use all popular vector-based drawing formats: DWG, DXF, corel draw (CDR), adobe illustrator (AI) etc... Some can also import raster files (bmp, jpg) for engraving (not cutting).
If you can do basic 3D, 2D is a walk in the park. It's just lines, arcs and connect the dots!
Youknowwho4eva has a good point about quantity. Especially if there is a set-up fee, shipping, or a minimum charge associated with the laser service.
Where laser cutters fall
flat on their face
is when your object has a bend, taper, or curve in the 3rd dimension. For example, if your medallions were rippled like a ribbon, instead of flat.