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What is the order of the positive and the negative Mitzvot in Rambam's Sefer Hamitzvot?

While some are grouped together, are they all ordered by any logic?

This question was sent by R. Tzvi Hirsh Segal Spitz to R. Yosef Dovid Sinzheim, and is recorded as Question # 5 in Kuntres Sheva Chakiros. R. Spitz began by questioning the order of specific mitzvot but then moved on to say that he could not find any order at all. He then went on and on praising Rambam's masterful writing in all areas, such that it is nigh inconceivable that he could have written Sefer Hamitzvot with no organization.

R. Sinzheim responded that it's basically impossible to answer this question, and in any event it's not only a question on Rambam but on basically all those who wrote books listing the mitzvot. He says that if the question would only be directed at Rambam, perhaps we could say that he had some stylistic reason based on the way lists of mitzvot were poeticized at the time, but since the problem extends well beyond Rambam's book alone, this doesn't really even help.

R. Spitz then responded that he disagrees with R. Sinzheim's claim that this is a flaw in all the works that list mitzvot, and he proceeded to explain the organization of some of them. He then added that even if the name issue existed for other authors, Rambam is in a class of his own, a shining star that comes forth once in a thousand years, whose every drop of ink needs to be explained.

R. Sinzheim then wrote back again, reiterating that there's no real way to know. He then adds that if R. Spitz thinks that the other authors actually had some form of organization then we can supply some semblance of order to Rambam's list as well. He begins with most of the mitzvot that relate to the early books of Mishneh Torah and then he lists all the mitzvot that relate to kodshim and taharot.

He concludes by noting that in any event the difficulty with everyone's order is that they didn't follow the order in the Torah.