Question: I've heard a lot of horror stories about PhD programs taking several years, and that US universities typically force you to go through many steps before you're able to be considered for graduation.

I'm interested in pursuing a PhD in the field of artificial intelligence, I already have a pretty thoroughly researched topic from my time running an AI company, data collected, and a partial paper written, but don't want to be stuck for years.

Does anyone have any experience making it through a US computer science PhD program in a reasonable amount of time?

Answer: 
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. 

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“If we knew what it was we were doing, it would not be called research, would it?” ~~Albert Einstein
PhD programs in the US very often are combined master+PhD programs with a planned duration of 2+3 years. In maths and computer science it is also very common that people take exactly that time. The horror stories you heard are more common in lab sciences like physics or chemistry. 

If you already have a masters degree you might find programs that allow you to skip the first 2 years but AFAIK this is rare. It is more common that the masters degree part consists of a bunch of exams plus optional courses with the implication that this part can be completed much quicker if you have the skills and knowledge to pass the exams without needing to take the courses. 

The three years of PhD time are meant for doing the research and writing a thesis. If your results are good enough this time can be reduced as well. In practice this could mean that after one year of research your adviser thinks you have enough results to write this up as a thesis and then you could graduate after another year. This happens but it is not very common. 

A PhD is a lot of work and takes a lot of time. You can't expect to come in with a good idea for a paper and then negotiate that they will award you a PhD for that paper.