As a former Nuclear Field recruiter, I never, ever saw an age waiver granted for the Nuclear Field.
That was over 10 years ago and things may have changed, but in my opinion, the chances are nil.
I don't think the manning situation will have any effect. When I joined (1979) the manning was low and I don't believe I would have gotten a waiver if I had been a year older (I was 24.)
I guess anything is possible and you won't know if you don't ask ...
Perhaps with your qualifications, there might be a Nuclear Instructor officer program you would qualify for. When I went to NPS, they had officers who came directly from the civilian community to teach.
I have no idea about the enlisted bonuses these days (I hear you even get one for going into the Nuclear Field), but I would not think that would be a consideration between going officer or enlisted.
If you are going in for the nuclear training, I think it would be better going the officer route. I was a chemistry major before going into the Navy, and, to tell the truth, the training at NPS isn't (or wasn't in 1980) very advanced, no matter how they describe it. Sure, unless you had some nuclear engineering classes, you're going to see some things that are new, but not nearly on the level of a junior level quantum mechanics class (or even sophomore level general physics).
Off topic: As a recruiter, I had an applicant who had graduated from UC Berkeley, GPA 4.0 in Physics, who wanted to be a cook. Of course, as a Nuclear Field recruiter, my job was to convince him he wanted to be a nuke. Being unwilling to use all the tactics normally associated with the typical recruiter, I was unsuccessful. In fact I don't think I could even convince him to take the NFQT. However, I did, eventually, convince him to take the DLAB (I don't think I was supposed to do that as part of my job description) and he went to boot camp with a CTI / Russian language program guarantee.
EDIT: I've been reading more on these boards and apparently the Nuclear Field incentives and waivers are much different from my experience. When I went to NPS in 1980 I knew of only 1 person above the age of 25, and he was former Army. So, my information is dated and inaccurate for your situation, including the assessment of the difficulty of the program. The periods I am describing are (1) after the draft, but before Reagan raised military pay, and before the time of enlistment bonuses, and (2) around the time of the first Gulf War with enlistment bonuses and a $25k cap on reenlistment bonuses.