There is a (relatively) low cost solution, a Roland MDX mill with mechanical scanner. It basically “probes” whatever it’s scanning by repeatedly prodding it, then can mill a replica out of aluminium or resin (or could mill a mould). Very common machines, a lot of schools/colleges have one, might be worth contacting some to see if anyone would do the job after hours or as a project with students. This sort of 2.5d job is ideal for such a system. Roland also make a low-cost laser scanner (Picza) but they are rare.
Alternatively as the design is probably quite basic (as most cap badges are) any decent modeller should be able to knock up a file from a straight on photo (not saying this wouldn’t take some time) as it’s basically just a 2d image extruded to give it a bit of depth. Then get someone to mill or 3D print the file.