I think if you lack connections in any industry in any part of the industrialized world, it's hard to find work these days. There's a biotech masters program where I work, I'm not involved with it, but I know they require internships to give students experience before they graduate.
I have temporarily trapped myself, due to the pregnancy. It's my second year as a postdoc, academic hiring starts each fall for the subsequent year. I won't apply for any fall 2016 jobs, because I wouldn't be able to complete the semester before needing to take leave. More than likely I will use maternity leave to apply for fall 2017 jobs. Thankfully, while there are some work culture issues, I'm mostly happy and treated well where I work now and I've been here over a year, so fully eligible for maternity leave benefits, which not everyone has in the US. Also, I do some necessary work - so even though a postdoc isn't really a permanent position, I have tremendous job security even if it's not the best job I've had in my life.
Are you able to omit the information about your advanced degrees when applying for other jobs? I had less than glamorous jobs between high school and my BA and my BA and MA and just didn't mention it before I was hired. I think the idea of being overqualified is absurd. Honestly, I've been working on some side projects - hope to finish this year with a programming certification, in case I get too frustrated with academia.
And I'll soon be 35! Delayed marriage and childbirth due to school. Was originally going to wait until I finished my PhD, but it was taking forever, large bits of it out of my control. So we just did it. We both finished school in 2014, but have been trying since 2012. It's still not the ideal time, but for a woman in science - there isn't one.