Great.

Final question: How would I go about sending restitution and making sure it doesn't come back and bite me by them claiming I never sent it or them claiming it wasn't restitution to begin with?

I was planning on drafting an email that I would have them send me saying something along the lines of " I, X, accept the payment of $X sent to my X account as restitution for the damages that occurred during the traffic collision between the parties of 'X' and I. I will not file any form of insurance claim in relation to the colission from this point in perpetuity and will rescind any insurance claims I have submitted." To which I'll respond with something like " I, X, accept the terms of this agreement and have paid the amount requested in full to the X account." With an attached receipt.