Fixed spelling as a concept—the very idea that there is a correct (and only one) way to spell canceling, for example—is an entirely modern notion. A spelling bee (or spelldown) would have been unthinkable before the sixteenth century and probably impossible to organize before the eighteenth. And acording to Bernard Comrie, the relationship between English spelling and spoken English is still more skunked today than what's found in many other languages.
That there should be such mayhem in English orthography reflects, in part, the old view about language—that writing is a visualization of speech, derivative, less real. The spoken word is what's full of possibility—of promise or of woe. Spelling? No, no, give us speech—all the excitement and thrill of the spoken word. The text was the thing that came after, later, if it came at all, which is one reason why Middle English orthography between 1100 and 1450 varies so much from one region to another—spellings approximated the sound or pronunciation of a scribe's region or the center of learning that bred him. Even within one manuscript, a single word might take ten different spellings.
What exactly is the link between pronunciation and spelling? If you haven't seen George Bernard Shaw's joke about ghoti being a perfectly valid alternative spelling for the word fish, Google it. Why should we spell cough with that nutty -gh and not a very simple -f? The word sounds like kof, after all. And in truth, there have been attempts in the not-so-distant past to reform English spelling along just these lines. Fortunately, they failed. Pronunciation spelling—if it were to become the standard—might make our beloved English even more unpredictable and chaotic than it already is. Especially in the South.
In short, English has been complicated from the beginning: it hardly got a moment's peace from invasions, migrations, plunders, and scepters—Norse, Roman, Norman, French, and more. Early attempts to improve orthography—like Thomas Smith's Dialogue concerning the Correct and Emended Writing of the English Language (1568)—were written in, well, Latin. Go figure. In some ways it's useful to think of English as a frontier language, borrowing and trading in so many other languages to stay alive. Some irregularities are to be expected, and some of them simply elude any satisfying (or useful) explanation. The mature editor simply points, instead, toward historical perspective and lets someone else worry about it.
All historical rambling aside, you can thank Noah Webster for the single consonant standard variation, canceling. It's an Americanism, Websterschrifte, or just plain bollocks (if you ask the other English speakers, the ones responsible for Old Speckled Hen and the Oxford English Dictionary). Webster is responsible for a great many so-called Americanisms. Why do Americans take the -u out of the word honour? Because Noah Webster taught us to. Why center instead of centre? Because he said so, and for a long time he's been the boss of us, the boss of our orthography.
This editor suspects the best choice for AMA editors is the single -l spelling, canceling. Remember that AMA style prefers Merriam-Webster Collegiate, and the first listing for each inflection has but one -l. When pressed for why—Why shouldn't we do it the Old Speckled Hen way?—the answer is that Webster's way is more common (at least according to Google, today*). The Webster way also allows AMA editors to follow a handy AMA-friendly rule about standard variants: Always use the first spelling of any two standard variants given in Merriam-Webster Collegiate. It's mere rule, yes, and thus a little cold and disappointing, true, but it pays off in consistency.**
But this is just a practical answer to the general question. A more refined answer will come once you've considered, carefully, the audience your company is writing for—the audience for whom you're editing—and the crucial question of whether or not the client has any preference one way or the other. Client trumps all, even AMA.
* Based on a Google search of the AMA Web site specifically. It should be noted that general Google searches of the Web return more hits for the double-consonant variants, which is noteworthy and relevant but not necessarily normative—especially for editors following AMA style.
** Chicago also recommends this practice (see 7.1, page 278).