Savage may offer you a settlement provided you're willing to sign a release of liability, otherwise the only way to collect is to file a lawsuit. If Savage has the firearm in their possession, you are in a less than ideal position to demand compensation, regardless of how it's orchestrated. If Savage demands the rifle to inspect, I'd propose sending it to a third party such as SSS, whom they know and trust, and whom the shooting community knows and trusts as well.

Hopefully your son's injuries will not be permanent, and he can pursue his ambitions without a compromised hand. Be smart, be reasonable, but be firm and I think it'll work out as best as can be hoped, for all parties involved.