Fischie22

I read that you're applying for Fall 2018, so you have time to retake if you want to.. I also read that you got 161/167/tbd, which is great! We got pretty much identical scores (161/168/5.0). Once you make the cutoff (I think your scores already meet the cutoff for TOP programs), whether you got a 170/170 or 161/167 hardly matters.. Your time would be much better spent on research (ideally securing a publication).
This is just my opinion.

I went to JHU for the first half of undergrad (EE major). I managed to get all A's my first two semesters with 17 and 19 credits, but had to study nonstop almost every day. The following semester, I took 18 credits, but decided to work a job and rush a professional fraternity. Grades dropped significantly (one A, mostly B+, one B).
Grad school classes may require more or less time than undergrad classes, not sure :/
JHU has such a beautiful campus, esp. in winter. BME facilities are also incredible.

Are you close to submitting a publication under your research professor? Seems like you've been working under him/her for a while. Ideally, before Fall 2017, you will have published or submitted 1-2 papers (conference papers or journals) for review. This way, you can focus on applications during Fall 2017.
I think that LORs from professors are usually the most well-received (please look this up to confirm), so your research professor is a great choice. From your description, I'm not sure if the staff scientist and manager can write compelling letters for you. Neutral letters may even be detrimental.
With publications and strong LORs, you have a good chance at top ME grad schools.
I am also new to the application process, and hopefully more experienced members here can give you advice.

Masters degree is definitely more manageable in terms of admission requirements/averages. 
As for research/engineering experience, you should work with your recommenders and tailor your personal statement to reflect the fact that you understand that you lack the background in engineering, but are passionate about becoming involved. Also, try to show that you have an ability, passion, and aptitude to conduct research - that is a big aspect of what grad schools look for in many cases. 
I come from an engineering background, so have only looked briefly into requirements of non-engineering majors. As I understand though, all STEM majors are treated about the same in the admissions process. 

First question is: Masters or PhD? Typically a masters program will have *slightly* lower admission standards from what I understand, which will influence your chances. A 3.3 GPA might be about average (or only slightly below) for many masters programs, but will be fairly far below for PhD programs from what I understand. 
As for GRE scores, if you get your predicted scores, the Quant should be pretty good, but the Verbal will be a bit low - should shoot for at least 157-160. Although a low Verbal won't ruin your chances, it can't hurt to improve it. 
Unfortunately your lack of research and/or technical experience won't help. Will have to ensure that you are able to demonstrate your ability to perform research with your LORs, etc.
As for programs, make sure you look at school websites, etc. to see if you will meet their GPA and test score requirements (or recommended requirements). Not super familiar with Petro or nuclear programs. There are some really good resources for finding GPA, test scores, etc. of students that apply/are accepted to programs (Magoosh has a lot of articles on related topics). I would suggest looking into this to narrow down the band of schools that you should look into. 
Hopefully this helps a bit.