I think the Panamanian tax exemption only applies to dividend income, not salaries. But I’m not sure, you’ll want to double check that with a Panamanian accountant.
Also, with a LLC you need to make sure it can pay dividends. I’m not sure if a US LLC can do that since it’s usually taxed on the member level. But otherwise you should be correct.
But again, it probably doesn’t work if you work from Panama. At least in theory. In practice they probably don’t care if all your customers are in other countries.