Being a former ET1 myself, with similar qualifications and degree, you are on the right path. I am an SRO with 2.5 yrs on shift, and almost complete with my shift manager quals.
Finish the degree, it DOES matter, trust me. don't let anyone ever tell you different, they are WRONG. Timing is everything, and be patient, and resilient. Apply, apply, apply. Utilize contacts you may have to push your resume, it may help. I understand you and your family have locations picked out, so if that is your number one criteria, be willing to take any job there to get foot in the door, and then after a year or two, you can always get into operations (NLO, SRO, etc), based on your performance, operations always recruits the best performers, and the best performers usually want into ops (pays the best).
Be sure you want to do shift work if you are putting in for operations. Also, understand that if you are going into an instant SRO program, you will spend the first 2 years in training, like going through nuke program all over again, although this time you will work MUCH harder. Be sure you and YOUR FAMILY are prepared for that. Just because you are a navy nuke, means nothing; I have seen ex nuke officers, 20 yr chiefs, degreed engineers, all types of ex enlisted nukes fail out of SRO classes, for all sorts of reasons, not always academic.
Another thing to remember when you show up day 1, the only things that matter are your ATTITUDE and your PERFORMANCE from that moment. No one cares about your past work, especially if navy nuke. You have to prove yourself with your actions. Get used to it, and get over it, and fast. It takes time to adjust to the civilian world, don't kid yourself. Be honest, and work on your people skills.
MTS doesn't matter much, nice to have, unless you are are applying for an instructor job, even then, it is more experience and interviews, so don't worry too much about that, instructor jobs are a dime a dozen lately. Start preparing for interviews. Study up on behavior interviews and assessment seminars (Exelon does this, as do others).
Learn how to sell yourself during interviews, have concrete examples on how you have demonstrated X leadership quality, especially if applying for management position. Don't BS, just be honest. Understand your weaknesses, and learn how to sell it, i.e. how you have or are working on the area.
Good luck, it was the best decision I ever made for me and my family. But be sure it is the right decision for you and your family. I work with a lot of retirees who get 2 checks every month, and I often think, "I only had to do 10 more years,".........yes, I made the right decision.
Good luck.