Something you ought to be aware of. A graduate of an ABET accredited school with a degree in electrical or mechanical engineering, and six months of seatime is entitled to sit for the USCG 3rd AE exam. You can get your national USCG license as 3AE with only six months of seatime. However, you need much more seatime to get STCW Officer endorsements
There are many inland and shoreside jobs for licensed 3AE marine engineers without STCW. Vessels under 200 Grt (that’s 90% of tugboats), fishing vessels, and all vessels on the Great Lakes and other “inland” waters.
If your degree in Mechanical Engineering is from an ABET accredited school, I suggest that you go get an entry level job as a wiper on an OSV or other vessel over 4000 Hp, and get 180 days (Only 120 days, if it’s 12 hour work days) of seatime. Then get your national USCG license as 3AE, and every QMED rating endorsement that you can with STCW.
Then you will be at a point where you have credentials and experience in the industry, and enough good job opportunities. On your time off take GMAT and GRE prep courses and make sure you get great scores on the exams. Next, you can reevaluate whether to go to sea or go back to school.
Just my opinion, but you might profit from a few years of work experience before going back to school. I also think you might want to consider engineering management and MBA programs at the best schools you can get into.