"However, in the second trial the small claims cap of $10,000 is removed and the judge can potentially award much more money in damages to the plaintiff."

This is wrong. $10,000 is the absolute damages cap in small claims court and the small claims appeal (which is really just a new trial). See California Code of Civil Procedure Section 116.220 and 116.221. The exact same claim is simply heard in front of a new judicial officer. It is not possible to amend the claim to add more damages in the appeal. See California Code of Civil Procedure Section 116.770(d).

A judge could award another $1000 but only if the appeal was frivilous. See California Code of Civil Procedure 116.790. This happens rarely.

* I'm a CA licensed attorney and just happened to attend the temporary judge small claims training just a couple weeks ago.