Question Regarding Career Change (Long)

I have a question and I'm throwing a fishing line out on the various message boards I visit to see if I can get some advice from those who have managed it before. I am currently dissatisfied at my job and I have been looking to change things up for the past year. I am currently an engineer/project manager in the oilfield with about 5 years experience. Currently live in Louisiana but looking to relocate to the Mobile, Al area to be closer to family. The problem is I am having a lot of trouble translating my experience from oilfield to other industries. I have tried several recruiting services and about the only thing they are good for is spamming my email about "IT Opportunities" that are little more than tech support. The last job I applied for through a service, I thought I had a chance to at least put my resume in front of someone but I called the rep I had been in contact with and she said that despite my resume looking fantastic, it would not even make it out of screening because I didn't have industry experience. She said my only chance was going through people I knew to find someone to take a chance on me. I have a BA in engineering (ME) and I just passed the FE back in May. I am looking specifically to move out of the oilfield and into heavy industry or manufacturing. Has anyone here made that kind of jump before? What did you do to make yourself more attractive to employers and get your resume on someones desk? Its frustrating. Thank you in advance for any help or advice.