Being dunned by ins corp for unsubstantiated debt

A woman abandoned her shopping cart against my door as we parked (WA is a comparative liability state and I can spell sine qua non). Opening my door bumped her cart into her REAR door, producing no damage. Weeks later her insurance carrier billed me for damage confined to her FRONT door and a RIGHT door. We refused, and her WA-based carrier threatened to report this "unpaid debt" to a collection agency (and thus the credit bureaus). Despite many letters up to and including the CEO asking them to justify their claim, they have made no attempt to do so, simply reiterating their threats of collection action and/or billing our carrier -- whom we have not identified to them -- for the alleged $755 damage.

I'm retired, wealthy, and angry, but even for a few thousand dollars I can't find a lawyer eager to pursue justice. My planned sequence is the state Insurance Commissioner, the A.G., and an attempt to have Small Claims Court dismiss the wrongfully claimed debt.

1. Should I forget the other party's several intentional contributions to her comparative liability and focus only on the fact that the cart touched only her rear door (only I witnessed the contact)?

2. Should I ignore their photographs that show damage incompatible with the shopping cart material, shape, and contact location and focus only on the fact that the cart touched only her rear door?

3. Should I just pay the SOBs off and fuhgheddaboutit because the little guy never beats insurance companies? (Tip: my 45-year win/loss record against FAR larger companies is 28:0.)

4. Isn't the insurance company committing extortion as defined by the Hobbs Act? ("Proof, schmoof: pay us or we'll destroy your 45-year-perfect credit rating.")

5. Other ideas?

I'd love to pose this question to the pay-for-an-answer system, but it apparently allows only a couple of sentences.
Any other ideas?

[judg4]

It allows as much space as you need...there is no limit

[judg4]

If any negative action is taken by any of them, you could take her and the insurer into small claims and based on what you say here, you would likely prevail.

...keep all evidence, witnesses etc. if any to prove your points!