There is no premium processing service available for the H4 EAD, I-765 application. However, you can submit an Expedite Request.

Change of status from H1B to J2 visa is a very rare case, usually, it's the opposite, people on J visas try to get H1B.

Current processing times for H4 EAD from all USCIS service centers, including the latest service request dates for standalone I-765...

If you are planning to apply for an H4 EAD for the first time, I'm here to help you step-by-step, right from the H4 EAD eligibility criteria

The following I-485 processing time for family-based adjustment of status is based on how long it took USCIS to complete 80% and 100% cases.