No promises here.....but I'm pretty sure you'll get nuke if you want it. I would be more worried about civil offences than waivers and what not.(ie jail, DUI, unpaid tickets, etc.....)
Your approach of hands on application of knowledge is dead on. I loved my job in the Navy because it was fun. You learn something new everyday and then you get to go out and play around with what you learned. I use the phrase "play around" loosely.....there are procedures, limits, and then more procedures. As I look back, I recall running drills as the best part of the job. You read and read about how the plant reacts to a certain set of circumstances and then the next day you get to see it with your own eyes.(Sometimes not as a drill

) I'll never forget my first scram recovery. I probably looked scared on the outside, but on the inside I was smiling in awe.
As far as the academic portion.....you appear to have a good head on your shoulders. I never spent a day in college and came from a corn field with a 2.69 high school GPA. Its all about dedication and desire to succeed. Waivers are just pieces of paper. Don't consider yourself a second class citizen in the Navy because of it. You'll be surrounded by guys/gals who all have a reason to be in the Navy. (bad college experience, family issues, money issues, etc)
So in summary, if you want it.....go for it. I can't speak for the recruiting end, but you should get nuke as long as you're honest with them. They'll do the paperwork because they need you more than you need them.
I did quite a bit of research before I contacted my recruiter although thinking back I could've done more. I signed up for AECF to get into DEP but I suppose I could've waited to sign the papers till I got my waivers done and a written nuke contract. Hopefully a fixable mistake on my part.
Should be fixable if your recruiter is worth his weight. Remember, they're held to a quota. Some rates are needed more than others. Nuke is needed. Tell him you really want to be a nuke.....if he doesn't budge.....ask to speak to the regional nuke recruiter. If he still wants to be useless. Call your MEPS and ask to talk to the regional nuke recruiter. The regional nuke guy has more influence than the guy at your recruiting station.
Let me know if this answers all your questions.