travelled on cap-gap extension.EAD expired.H1B approval.Can I return

Due to some reasons ,I had to travel on Cap Gap extension period. My EAD expired. But I had H1B approval.

Can i return back to US ? I checked online, it said I can’t.

So can i re-apply for H1B under cap exempt ? or any other way. like by getting it transferred to another company or anything.