You can only work for your H1B sponsor in order to keep the H1 status. If you use EAD (any kind), it means you give up your H1B status.
The right way to do this is to apply for another H1B for your part time job. This way, you can work for both employer at the same time.
The right way to do this is to apply for another H1B for your part time job. This way, you can work for both employer at the same time.