Don't worry about not having a degree. You meet the qualifications for the SRO program. The lack of degree might matter later on, but not right now.
Don't limit yourself to a single plant either. If you do that you're probably going to end up disappointed. That being said, check out the military job fairs in your area. When I retired there were several utilities that had people at them.
I've said it before, but I'll say it again. Go to the NRC website. They have a map showing the locations of all the reactors and the company that owns them. Find a plant you're interested in and put that company's careers section on your list of things to look at each day. Go ahead and set up an account and upload your resume, that way when a job opens up that you're interested in you just have to click "apply".
When are you really getting out? I ask that because 7 months from now is near the end of the year, and from what I've seen the hiring tends to drop off in the Nov / Dec timeframe. The holidays tend to slow everything down...
Another thing to keep in the back of your head. This is going to sound mean, but I don't mean it that way... Your Navy quals mean you meet the minimum requirements for the job, nothing more. There's a LOT to learn about these plants, and a lot of it you've never seen before. If you get hired on as an SRO you'll get 6 months onsite to start to learn the plant. Use that time wisely! If you decide to sit around and tell sea stories all day you're going to rapidly be left behind by the people who actually went out and learned the plant. It can be done, but from what I've seen it's about a 10% difference in GPA...
Good luck, and thanks for your service! Feel free to PM me if you have any questions.