let insurance handle it

understand your reasoning that he should repair only the portion damaged caused by you, well in reality any shop will either repair the entire bumper or replace it with a new one (cover).  let your insurance handle it, most likely your insurance will pay him about 500 based on what you said.  you can show your photos to insurance but it may not make a difference.

you will not have a record and your premium will not be raised so no worry.