Sorry to be blunt, but I don't think you have any clue about the competitiveness of finance PhD admissions or the difficulty of coursework in a finance PhD program and you are aiming far too high.
For any finance PhD, let alone a top 20 your application will pretty much be ignored without at least linear algebra (which you don't have) and calc 3 (which you do). This is the bare minimum you will need to survive your first year classes and pass quals. To get into a top 20 finance PhD program with a US BA -even from a top US public university- you will probably need real analysis. A serious calc based probability class will help. And even with that, without excellent LOR's from finance or econ profs, your chances at a top 20 will be small.
Let me put it this way. I am PhD student in finance at a top 50 program. Of the 16 students in the program, I know that at least 5 came in with a masters degree in statistics or quant finance from a major US research university and at least 3 more have masters degrees in econ or finance from very good international universities.
The lack of publications will not hurt. Very few incoming students have any serious publications. However, many do have some sort of RA experience, which you have, though you are not clear about how much work it was and what your role was.
Honestly, I would suggest you take a couple of years to do either an MA in econ at a US university that has a history of placing students in finance and econ PhD programs, or to try and find a research assistant position in econ or finance at a prominent b-school, NGO, think tank, govt agency etc, and take classes on the side. As a veteran, you may get some sort of preferential treatment at some government jobs, though I don't know. It is my understanding that while this was not true in the past, at the current time officers are eligible for some GI Bill educational funding.
Doing a masters in quant finance or math finance is not a good option for you since without linear agebra, differential equations and some programming background getting into a good program that can place students in top 20 PhD program will be too difficult. And I think doing an MA in econ at a school with a history of placing students in PhD programs is a better option than an MA in statistics.
Also, while I am not as familiar with these programs, there are a few PhD programs at Public Policy/ Public Affairs/ International Affairs schools that offer some sort of economics concentration and have faculty doing work in international finance that could serve as your advisor. These programs usually have slightly less strict math standards for incoming students -though I would still take linear agebra- and your military experience especially the operations coordinator work would probably be seen as a strong plus at many of these schools. You would have to search very carefully since many of these schools PhD programs concentrate on international development or are more poli-sci oriented, or have an economics concentration but don't have faculty in international finance.