[personjerry]

Agreed your CV probably needs work. But talk to a recruiter in the industry to help you improve your resume, they know far more and have more accurate knowledge than another engineer. Also, not sure how many positions you've applied to but apply to as many as you can, 100 would not a bad number of positions to apply to. It can be a numbers game.

To answer the question in the title - No, you shouldn't. For the same reason if you google "employer counteroffer" every piece of advice will advise you not to take the counteroffer. You've already signaled your intentions and they will no longer see you as aligned, crippling future growth at the organization, and they will oust you once they can.