What type of J1 is you J2 based upon ?
- If the primary visa (J1) holder has a 'foreign presence requirement', you will not be able to change from J2 to H1b until your primary visa holder has obtained a waiver.
- If the primary visa holder doesn't have a foreign presence requirement, you should be able to change to H1b without major problems (they might send you a request for evidence to provide an 'advisory opinion' from the department of state before they allow you to change.
You are saying 'continuing on EAD'. What is your EAD based on ? Do you have a GC petition of your own or are you a beneficiary of your spouses petition ?