Let me go out on a limb and assume that the question you really want answered is twofold. Can I do this? How?
In the US, the essential core of a doctorate is the ability to pass a set of qualifying exams and production of an acceptable dissertation. I got my degree from a place where those were actually the only requirements.
Yes, there is a lot of coursework in a typical program, but it is there to enable you to do the other things, not for the essence of the coursework itself. In some places, not all, everything else can be waived beyond the two essentials. The qualifiers are there to assure that you have sufficient breadth in your field. The dissertation is so that you show both depth in a subfield and the ability to successfully do research.
So, the first requirement for you to finish in two years is to find a professor willing to "advise" you and judge your resulting dissertation. If you can do that, and if you are already prepared to pass the (quite difficult) qualifiers, then you have a hope of success. Finding that advisor, however, will take some effort because not everyone will want to agree. I think that few will, and none will make you any guarantee that you finish on a schedule. You and that professor will also need to convince a committee that the dissertation is adequate. Normally that isn't a problem if the advisor is happy. Note that all of this is true if your advisor doesn't need to give you any actual advice. Some students are self-organizing enough that it isn't needed. But the advisor's acceptance of the thesis is still needed.
But the harder requirement is the dissertation. Having a good problem and having done some research on it (partial paper...) is good, but gives you no guarantee. Whenever true research is involved there is no guarantee as to when it will reach fruition. You are stepping into the unknown and, well, it is unknown. Some problems that appear doable from the outside are devilishly difficult once you open the door. Others that seem substantial turn out, after a bit of work, to be trivial and not worth the effort. (I've personally worked on both of those sorts of problems.)
So, with hard work, and your obvious head start, you have a shot of finishing sooner than others would. But, still, there is no guarantee. Don't organize your life as if there is such a guarantee. You need diligence as well as flexibility to be a researcher.
“If we knew what it was we were doing, it would not be called research, would it?” ~~Albert Einstein