Is the extended OPT specific to an everified employer or you can switch employer after getting the new EAD? It may not work and I really don't know anything about it, but this is just a wild idea:
1. Before your current EAD expires, contact e-verified dhoti consultancy and get a job offer
3. Apply immediately for extension using that job offer (from everified consultancy), but never join their job.
3. Use the new EAD card to continue current employment after your current EAD expires.