Well, I have to agree with Taylor, that I would recommend ROTC, and enjoy your college time. As far as someone saying that Being in the Academy will be better for your career, I am not certain about that, all i know is that my last 2 Reactor Officers were both ROTC grads, and there area a lot more ROTC officers, either from the ROTC 4 year programs, NUPOC selectees, and prior enlisted STA-21 officers, then there are Academy kids. In this day and age, with the majority of the Officer Corps being out of the ROTC program, some of the old prejudices have gone away, or even been reversed.
As far as getting into the Nuclear field, whether you go to the Acadamy, or ROTC, either way, you have to show a high level of technical copmetency, and you have to have a personal interview with NAVSEA-08 (Deputy Secretary of the Nvay - Nuclear Power) to become an officer in his reactors. This is something that happens to ALL nuke officers, even Warrents and LDO's. In the end, he has the final and only say if you become an officer in his navy. (And believe me, it IS his navy).
Your ASVAB will not matter, but the higher your SAT or ACT Scores, the better, because those DO have a definite impact, and sometimes a person with a little lower GPA (Although from the Officer recruiter side, a lower GPA right now is still talking about a 3.1 college GPA) will get a boost from high SAT or ACT scores. I know the scores you are putting here, if both Verbal and Math are 34 or 800, then you have got great scores, and as long as you perform in college, whether it is at the USNA or ROTC, you have a definite chance to become a nuclear officer.