RE: The SSA only allows you to e-file the W-2 Copies A and D forms (includes all employees) once.
This is not correct. You can file in batches. As long as you don't file the same employee's W-2 more than once, then there is no issue with the SSA. In fact, if the an employer is large enough they are required to file using multiple submissions - per the instructions which are easy to find online.