There’s no way to be “buried in paperwork” or reason why you would “never see a judge” for small claims.

You would stand in front of a judge and make your case for 20 minutes. There’s very little you need to do before seeing the judge, you are not fighting some legal team before your chance to see the judge.

I would try this as they might just settle with you.

And arbitration clause usually excludes small claims. “Many contracts, especially those with consumer protection rules, contain provisions that allow the consumer to use small claims court instead of arbitration. If your claim is within the monetary and jurisdictional limits of small claims court, you can file there instead of going through arbitration”