Background: started my career at Chevron. Elected to move onto a public E&P that was subsequently bought out.
Observation 1: It's actually a solid labor market right now for people who have worked for independents. There's a bias that they have better commercial skills, are more up to date on best practices, and are harder working (vs those at majors).
Observation 2: Recruiters get really excited about talent post merger. Everybody is looking for a job, and you don't have the adverse selection problem whereby weaker candidates are typically the ones looking. (If somebody is recognized for being good, why would they quit?)
Reach out to your network and own the merger. Chances are you'll find a new, great role. And, down the road you'll have one he-l of a network (Hess people will be everywhere).