Terrific question and I might have a hint.
The letter ר in Hebrew Rabbis titles might stand for two options: either רב or רבי (also רבינו). Although רב accepts the definitive article הרב, the other does not.
When referring to Rabbis, if the "original" acronym stood for Rabbi like Rabbi Shlomo Yitzchaki, it could not accept the article, whereas the "original" acronym stood for Rav, it could accept the article. THis is similar (somehow) to the difference between the Tanoim (Rabbi Akiva) and the Amoroyim (Rav Ashi). I would say it is the difference between undisputable and disputable.
The keyword here is "original". It is clear, that the use of those acronyms is traditional, not institutional. So seemingly, if a Rabbi was well respected, he might be called Harav (the level of the Amoroyim), and therefore הרמב"ם, הריטב"א, הרן etc. If he was perceived on a "higher" paternal level, he might be called Rabbi, like Rashi that was accepted unanimously.
Correct me if I'm wrong, but it seems that in English it is impossible to use the definitive article with Rabbis acronyms in any way, because in English, unlike ה in Hebrew, "the" can not be used with a title, like The Rabbi Berkowitz. So we can say הרמב"ם in Hebrew meaning הרב משה בן מימון, but in English it is wrong to say The Rambam, as it would mean The Rabbi Moyshe Ben Maymon.
The usage of the article when referring to the name of the book a Rabbi is known for, like החפץ חיים, הט"ז etc is actually acceptable. Like "the [book of] Chofetz Chaim"
Nb: As a native Modern Hebrew speaker, I do see a "very large degree of freedom" in the usage of the definitive article in the Oral Torah (so to speak, if not explicit mistakes), from the Mishna, through the Talmud and to all of the commentators and interpreters till today. So a lot of differences in the spelling of the names can be explained simply by inaccuracies and inconsistencies of the authors.