Scientist to Engineer - Applying to PhD Programs. How can I prep?

[maxzilla]

Hi everyone. I'll try to keep this short!

I graduated this past winter with a dual degree (BA, my uni does not offer BS) in Earth Science and Architecture, along with a minor in Visual Arts. I desire to study Mechanical Engineering and/or Applied Physics, and will apply to PhD programs commencing in Fall of 2020. I had applied for Masters programs in Mechanical Engineering, including LEAP, this past season (commencing Fall 2018) but was rejected by all three I applied to. 

I have a low GPA from my main university (3.0/4.0), but I have 4.0 and 5.0/4.0 GPAs from two other universities where I took summer classes/conducted research in my senior year. All of my undergraduate years aside from the senior year (5th year in undergrad) were dreadful for me. I encountered an incredible amount of turmoil in my personal life and at university that really impacted my academic performance. It was definitely the darkest period of my life (I won't get into specifics here). 

In my senior year, I made some drastic but necessary changes to regain control of my life. From this point on I was able to focus entirely on my work with few distractions. I participated in a lot of research in multiple areas (bio-optics, dendrology, ecology, classical geology surveying, data analysis/MATLAB, GIS, etc.). I've done a lot of interdisciplinary work as well as lab work and field work. This is when I fell in love with engineering. I have not been published but all of my professors from this period love me -- I was selected to teach in my main uni's ES department, and I was also nominated for a USGS internship. I also achieved 'honors' standing at the other university I conducted research at. However, all of these positives have done very little for my GPA as it was in the 2+ range prior to my senior year.

My GRE scores are 160 Q, 165 V and 5 W. I intend to test again to get a higher Quant. score. For my bachelors I had a few courses in common with Eng. majors: Calculus 1 and 2, Calculus-based Physics 1 and 2. My personal statement emphasized growth and my reasons for wanting to pursue Mechanical Engineering, namely combining and applying what I've learned from the fields of Earth Science and Architecture. Recommendation letters from my previous attempt were written all by professors who I have done research with, one of them I taught under for one year.

Since evidently I was not qualified enough to be accepted this year, I am devoted to enhancing my application for the 2020 admissions. Currently I feel that my weakest point (undergrad GPA aside, which is something I cannot longer change) is my lack of engineering experience. However I have ran into a lot of difficulty with finding an engineering related job, as I do not fulfill the requirements for them. I also intend to take more engineering courses over the next few months, namely Diff.Eq, Thermo, etc. Additionally, I will be studying for the GRE Subject test in Physics. 

Do you think the latter two options (taking courses and tackling GRE Physics) will be adequate? I want to do everything that I can to maximize my chances. Ideally I will find some sort of engineering job in addition to attending classes. This is likely the last chance I'll get to apply to graduate school, and I want to make it work. 

I would greatly appreciate any insight or feedback you may have, especially if you (or anyone you know) has made a similar switch in fields.

Thanks in advance.