Your new employer will be responsible for your new FEC. Since your SAFEA contract and FEC are tied to an employer, and your relationship with the employer has been terminated, it leaves things in an awkward situation.
Ultimately, it will depend on how much influence/expertise your new employer has and how badly they want you.
If your employer is on fairly good terms with the local powers that be, the Letter of Reference can be explained away.
Also, some employers do not use SAFEA and hire via the labor board as a way of streamlining hires.
So, I think your best bet is discussing the situation with your new employer and let them solve any problems. This will all get sorted out locally where you new employer is.
My first suggestion however, is that you simply transfer your FEC to your new employer. That should make everybody happy.
I wish you well.