Non-Muslim sources were not subject to such pressures, but they by definition look at the situations from the outside and not the inside, and are much sketchier.
The standard biography says Muhammad died in his wife's house, after carefully making sure Bakr was understood to be his successor. Before he's buried there's a contretemps with Umar, who refuses to admit that he's dead until quelled by a never-before-heard quotation from the Quran by Bakr (or by somebody pointing out that the body is starting to stink, according to a different tradition). In either case, this is before the great push into the north.
Yet there are non-Muslim sources and traces in some Muslim traditions saying that Muhammad was with his conquering troops as they started up the Levant. And these also tend to say that the Muslims required very little beyond tribute and a profession of monotheism--at the time.
Plus there's evidence that the first center of worship, or at least a major one, for Muslims was Jerusalem and not Mecca. I reviewed a book addressing that thesis last year.
Shoemaker suggests that Muhammad died 3 years later than the canonical date, that he had been with armies heading for Jerusalem, which I gather they wanted to capture to "immanentize the eschaton," that he believed the end of the world was coming very quickly, and that when it didn't, a process of re-interpretation and tightening the standards for what it meant to be Muslim meant that later Muslims wound up revising the chronology to put Muhammad's death and the holy place back firmly into Arab land--far from the other monotheists.
He can't prove it. Nobody can, with the data at hand--nearly everything is either a rubber ruler or not relevant. The Quran has very little about Muhammad, for example (and there's evidence that even that wasn't fixed yet), and the relevant sira and hadith are generally flimsy and false.
He argues bitterly that given the mountain of speculation about Jesus, despite a plethora of documents, similar speculation about Muhammad and the development of Islam is not just allowable but reasonable given the scarcity of reliable documents. (He seems to think the Jesus Seminar is scholarly. Composed of scholars, yes--scholarly in approach, no.)
It looks as though the direction of Muslim worship changed, if grave and architectural evidence can be believed, but the why is not easy to prove.
As to Muhammad's death year and place--maybe these were reinterpreted for religious reasons, or maybe Umar suspected something was amiss--and it was, and it was covered up. (Utter speculation on my part.)
I read it so you don't have to.
I heard his book on Marian devotion was out, and discovered this one in the library along with it. Twofer deal.