Like you I cannot find any references as to why there is a distinct pronunciation differences around the "o." All I can figure is that it is simply a mutation that has simply "suck"stuck." More than likely it has something to do with the reason why American accents are considerably different than British accents the speed in which they diverted.
This is more about the letters around it. The letter "h" seems to have problems in many languages, and especially so in Romance languages. The French have been ignoring it for centuries! Both in English and in German it is generally pronounced as a breathless letter. Consequently it tends to make the next phonic sound "longer." For example Hard and Card. The "h" makes Hard take longer to say and you can really hear the "a" appose to Card which can sound more like "Crd." Then you have the "l." This adds to the already overly stressed "o" to make sound even more like "awl." Take words like all, null, and doll, they all have an "wl" sound to them when pronounced. So overall the "dark l" is what is causing it, but with significant help from a breathless "h" to make it a definite "awl."
I'm going to combine #3 and #4 since they have the same answer. British pronunciation in dictionaries use the /ɒl/ and no variation and American pronunciations use mostly /ɔl/ to some variation. I would assume that would mean that it is fairly resent that the "common" pronunciation is "awl" but it has be significantly different from the British since the deviation first start. This will come down the how the speaker pronounces the "h" as to how close to "a" the "o" will become, causing the deviation in the phonetic key.
We are back to the vowel + dark "l" combination again. With the syllables separating the "l"s in the American pronunciation you end up with "col" and "mol". Both are pronounced with the "wl" but with the lack of "h" makes it sound like /ɑl/.
Overall Americans pronounce "ol" with an accent that is very similar to "awl." The differences being literally technicality, which can be seen in the dictionaries. All of them are using a different phonetic alphabet meaning the exact characters' pronunciation equivalents are up to debate. Considering your MW dictionary uses a different one than the one I found online at their website. As for refences to the British pronunciation I used dictionary.com. Which shows every "ol" combination as /ɒl/.