It looks like the bottom of the emblem was straight, so I think there are 2 breaks.
Try this, line the emblems up on a ruler so the bottom is straight.
Then as close as 90 degrees to the table top as you can get take a picture, with the ruler, it provides scale. Also if you can have a solid color background, not white as part of the emblem is white.
This image then gives you a good pattern.
Now, talk to a sign shop, they do graphics, they can work with the image, or the emblem if you have it with you. They may have the ability to cut it out of plastic, (laser cut or cnc router) or know someone who does.
Another option, look at the Glowforge forum (I'm sure there is one somewhere) its a laser cutter that might work well for this. See if someone has one near you. A paid hobbyist might be the ticket, they get to use their cutter on a new project, you get new emblems. trust me people that buy a laser cutter live for a new project.