Since this is a property damage case I think you will find it hard to get an attorney willing to represent you on a contingent fee in a case with limited damages. You would be better off paying an attorney for a consultation to help you out. Keep in mind that it may not be worth the headache of a large claim case for just $1,000. You could probably save money in the long run by filing a small claims case for the $6,000 max.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.
This is a tort claim against the driver of the vehicle that hit you. The cost of handling this type of claim can be difficult to justify where the damages are limited. An attorney could spend a good 10-20 hours on the case, depending on how far it goes in court. At $275-350/hour, you could invest most or all of what you have at stake before you receive it. While you can also recover your attorney's fees against the defendant--which would have to be paid by the insurance company--if you prevail, the remaining question is whether it's worth the trouble.
You would probably be better off paying an attorney a lesser fee to help you put together what you need for small claims court.
This answer is intended to provide general guidance only and does not create an attorney-client relationship. Please consider retaining legal counsel if you remain uncertain about your rights.
This is a tort claim. You may want to consider filing in King County Superior Court, then moving the case into Mandatory Arbitration (available for disputes valued at less than $50K). However, a contingent fee is typically in the range of 1/3 of the amount recovered, so you should expect to ultimately receive much less than the $7K you want, even if you prove your case. I suggest you ask the defense insurance adjuster to agree to mediate the case before you file it. You may be able to resolve it that way, cheaply and quickly.
I doubt a lawyer will do a small property claim on a contingency fee basis, but perhaps you can find a newly-licensed attorney to help you resolve this cheaply.
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I agree regarding the use of the court. However I think the filing fee is about $241 now, plus $50 or so each to serve the Summons and Complaint. To that be aware that the rules also require that the plaintiff pay a $220 fee when filing their statement of arbitrability. There would no doubt be other costs. I just don't want you to get sticker shock from some of these court costs.
I have concern as to the suggestion that bringing a superior court action would be wise if this is just a property action (no personal injury) under $10,000 in value. I would certainly consult with a local attorney in your area before even trying that tact and make certain to ask them about whether there is a statute that shifts attorney fees in your circumstance. The first thing I would be doing if you were to cold call my office (after conflict check of course) would be to ask you if you had tendered this (or even discussed it) with your own carrier. Sometimes, even if you are not covered for the issue, friendly claims handlers can sometimes intervene and talk to the other adjuster on your behalf. The next thing I might suggest is that if your evidence that USAA has grossly undervalued your property damage claim, that you look for an attorney who indicates that they may perform bad faith insurance related claims and find out what is happening with USAA in litigation around the country or state. You should be prepared to tell them how long it took between the car accident and when USAA contacted you about the matter to discuss and settle your property damage claim. With no personal injury claim associated with this I do think you are probably limited to a small claims action and most local attorneys in your area should be able to meet with you and tell you the basics of what you would need to do - including the information about who to sue and the time limits of your claim within one or two consultations.
You may be entitled to bring an action in the WA Superior court, however you might need an expert to evaluate the diminished value portion of your claim. I understand your frustration and have dealt with this issue numerous times. Usually once the insurance company has your expert evaluation which will lay out your diminished claim they will increase their offer.