I would suggest starting over with your assessment of your options, because I don’t think you’ve received, so far, enough quality or quantity of information.
I will begin with the teaching career.
What I have found today searching for teacher jobs online shows your education professors’ statements to be far from true.
When I searched “teacher” on the jobs site Indeed.com I got a phenomenal 100,000 results (2,750 when limited to New Jersey). I looked at many of the results and saw no more emphasis on science and math than in the New Jersey teaching credential requirements (http://certificationmap.com/states/new-jersey-teacher-certification/#req). Other sites I looked at were www.teachers-teachers.com, www.k12jobspot.com, www.jobs2careers.com and www.ihireelementaryteachers.com. Because the Bureau of Labor Statistics (BLS) (http://www.bls.gov/emp/ep_table_102.htm) predicts more job growth and openings for elementary and middle school teachers (12% growth & 684,000 openings in 2012-2022) than for high school teachers (5.55% growth & 340,00 openings in 2012-2022), I particularly looked at elementary and middle school jobs. (BLS’ predicted job growth average of all occupations is 10.8% for 2012-2022.) By the way, the BLS remarks that, “Opportunities will vary by region and school setting. Job prospects should be better in the South and West, which are expected to have rapid enrollment growth. Furthermore, opportunities will be better in urban and rural school districts than in suburban school districts.” According to http://money.usnews.com/careers/best-jobs/elementary-school-teacher, the national unemployment rate for elementary school teachers was 3.1% in 2013 or later, decidedly below the average for all occupations. Incidentally, a lot of applicants for entry jobs isn’t, I think, all that significant, because a lot of people (who weren’t well aware of what it would entail) become disenchanted with the profession, or at least in certain areas.
If you like the idea of being a teacher (do research on what it entails, e.g. http://www.huffingtonpost.com/randy-turner/a-warning-to-young-people_b_3033304.html and the comments at the bottom of http://www.pbs.org/newshour/bb/todays-newest-teachers-face-tough-job-odds-high-turnover/) and you’re prepared to move to another part of country likely to need teachers especially, it makes sense to see how much work you would have to do now to get a teaching credential.
(It should be noted that instructors have no qualifications for giving career advice in their field other than their own experiences, the experiences their colleagues might have shared with them and what they have picked up in publications, meetings, websites or other communication media they visit. These sources are likely to be dated (obsolete), based on little data and absent of objective data analysis.)