What should I do next?

I have been looking for work for a long time now. I have only managed to secure internships due to my lack of experience (I graduated BSME 2010). Most of my undergrad work was for the school's IT office, and now that I want to get into product design I am having a hard time.

I have uploaded my portfolio for critique, but I usually get that it's not suitable for ID firms or similar roles.

I'm not sure what to do.

Should I go back to school and study electrical engineering? I don't have a family or anything, but I'm concerned about going into more debt.

I am not sure if I should stick it out w/ my current contract position in hopes that they hire me next year.

It seems that my resume is only fitting for lower level IT or the occasional support engineering role. I feel like my options are incredibly limited.

Should I start over and get another BS - this time BSEE?

Is it possible to become a systems engineer w/ a mechanical engineering background?

In most places that I have worked with EE's and ME's you are expected to start somewhere.
What this means is that you don't start as a ME designing in the Engineering dept.
If I were you I would type Mechanical Maintenance and variations of that in to the search and apply.
Then once you are within some company in the maintenance dept you can start applying to their engineering dept(with experience, theirs).