Why not leave bridges to hold the parts in? With MDF you should be able to take a Dremil and zip the parts out in seconds. Then use a small upright belt sander and knock any leftover off.
I don't know what software you're using to do your CAD/CAM but something like VCarve Pro (if your stuff doesn't need 3D) is very reasonable (about $600 US) and it can leave tabs. Cut as many parts as you like and as long as your major material holds down, the small parts stay in place.
$600 has two less zeros than $20,000.