Q. Shouldn't I be able to get full credit instead of the lifetime learning credit (LLC)?
A. No. There is no special provision for that situation.
As a W-2 employee, you're no longer (since 2018) allowed a deduction for job expenses (such as licenses and certifications). Even in the "old days", the LLC would have been a better option than a job expense deduction.
A self employed person would be allowed a business deduction, which would only be slightly better than the LLC.
I assume you're not eligible for the American Opportunity credit.