What advice would you give someone wanting to be a competitive applicant to a nursing program?

The AECP program site lists a bunch of programs that meet its prerequisites. There are programs in the NE as well, in fact I think the Nursing School in Vermont meets the prerequisites. But, it's not about location. You're on active duty for two years, it's a job location, so you take which one will accept you.
As for your question about the courses, you have to identify schools you want to attend and look it up. As a general rule, schools will accept courses from another regionally accredited college that result in a letter grade. Some schools are a bit weird about accepting online labs.

Have you looked into ROTC? Many schools have an ROTC program which pay you to attend, pay your tuition, and you would commission upon completion.

The Army AECP web site is pretty clear. It has a list of colleges and universities. As far as your taking general education and other classes to achieve "junior" standing, so you only have two years of nursing school left for your Bachelors Degree, I would recommend a community college in your local area that is accredited so that its education credits are normally accepted by the major universities in that area. My wife took most of her general education classes at our local community college, transferred the credits to the University of Missouri, St Louis, and completed her BSN at Barnes School of Nursing. UMSL took all of her credits from the Community College.

Talk with the counselors at the Community College. Some remedial courses are not transferable. These courses are set up to help students who failed to learn to read, write, or do simple math, but graduated from High School.