^Con’t from above:
The easiest way to get all three of these things is doing an MA program in the target field. You will still have to take some foundational coursework as a non-degree student, but you can get away with taking fewer classes because MA programs usually have less stringent requirements. While you’re at the MA program, you’ll take graduate-level classes in the field; you’ll work directly with faculty members on research and get two years of research experience; and you’ll also glean those letters you need. And like I said, if you serve a full term of active duty in the military your GI Bill will pay for your MA (although some academic MA programs in physics come with funding). The Navy may even send you to graduate school so you can come back and be an astrophysicist or oceanographer for them - the Navy has a great need for scientists in those fields, and Naval service as a scientist can help you get into NASA (or NOAA, as the case may be).
Also, what I said above was geared towards PhD programs. You need all of this stuff but less of it if you want to go to an MA program - you’ll still need some courses (but may be able to get away with 5-10 rather than the 10+); you’ll still benefit from some research experience (but maybe 1-2 years will be enough rather than more). You’ll also still need the letters (but all three could be from professors who’ve only seen you in class rather than in your research internship). Of course, the more of it you have the more competitive you’ll be.
Finally, you asked about programs in which you can take prereqs. There are some of those out there - they’re called post-baccalaureate programs. For example, Pittsburgh has one called the [Hot Metal Bridge](Hot Metal Bridge Post-Bac Program | The Dietrich School of Arts & Sciences Graduate Studies | University of Pittsburgh) program. Columbia also has a formal one, although I think it’s limited to alumni of their undergrad colleges (and I can’t find the website, because I don’t remember what it’s called).
However, even at schools that don’t have their own formal post-baccalaureate programs if you have the resources you can cobble together your own either full- or part-time. For example, Columbia’s School of Professional Studies (their continuing-ed, non-degree division) has a whole page about [preparing for graduate school](Academics | Postbaccalaureate Studies Graduate School Preparation | Columbia University School of Professional Studies) since a lot of people take non-degree classes there in order to prepare for PhD and MA programs. They have a few structured certificates but they also have a postbaccalaureate studies team that will give you advisement on applying for graduate school. Many schools have a division set aside for continuing ed that may have this kind of support, so I’d hunt around. It would be awesome to do a post-baccalaureate program at one of the schools at which you are interested in completing a PhD, too.