I was under the impression that most homeowners policies covered you against accidental shooting lawsuits
It is NOT an “accidental shooting” if it was self defense.
Self defense is an affirmative defense.
You are admitting to assault with a deadly weapon or homicide.
You then point to the justification of self defense.
If you fail to make the self defense argument, you get convicted.
Since a self defense shooting in an intentional act, and not an accident, you have to let your attorney deal with the insurance company.
Your homeowner's insurance does not cover you if you burn your house down on purpose, any more than your auto insurance will cover you for willfully crashing into the neighbors car.