You're story doesn't really make much sense. For starters, Los Angeles does not have an income tax (and indeed, no city in CA does, as that is illegal under CA's constitution).
When I got someone on the phone they refused to admit that there could be any way that I, a non-resident who never set foot in the state that tax year, could claim that my income wasn’t subject to their tax regime. Nope, it’s all California source income.
If you've never lived in CA you wouldn't have owed income tax on more than the portion of the salary you received for the few days you were in CA, and certainly not tens of thousands, unless your employer claimed you were a CA-based employee. In which case your beef is with your employer, not with the CA FTB, as the FTB is merely relying on the documentation provided by your employer.
And they make their documentation as confusing as possible, dark patterns at their best.
As a tax lawyer, I deal with the FTB pretty regularly. They're usually helpful, and the agents I've dealt with have been remarkably easy to work with in addressing penalties, past-due taxes/returns, etc.
Never could figure out how to get my money back from Los Angeles.
Why do you think you paid money to LA? LA does not collect income taxes.