I'm in the same situation (except I'm still interested in pursuing further study and don't have any regrets of having studied physics).
To answer the thread's question: get a graduate degree in something if you can afford it. I hate to be pessimistic, but it looks like the only way you'll get an engineering job in this climate is if the employer can't find anyone with an engineering degree for the position that isn't a convicted felon or if you have some serious contacts that will overlook your the fact your degree says physics instead of engineering.
99% of job offers with the word "engineer" over at usajobs, monster and individual company websites that I thought a physics BSc might have a chance at (telecom/RF and optics companies) don't invite for anyone with science degrees to apply. You should still try applying to things you feel somewhat confident about even if they're meant for engineers though, an online application and modding your CV for the job only takes 5-10 minutes.
A sibling of mine with contacts in the telecom industry is forwarding my resume all over the place without much success so far. If you don't know a specific work-relevant techniques like "power engineering" it is hard to convince a business you can do the job, much less make it through the resume filters on online applications.
If you're a US citizen, look into the Dept of Defense and Dept of Energy jobs(national labs), defense contractors(Boeing, Raytheon, etc.), government institutions (NASA, environmental and meteorological agencies), and 3rd party environmental consultants.
Just my opinion, but I wouldn't spend any money on certifications from random institutions unless it's something that is truly "official", recognized and transferable, like a reactor operator license, license to operate heavy machinery/vehicles, security clearance for government jobs, etc.