I have been reading lots of articles about this lately and it seems all the written source material is from at least 100 years after the prophet's death (although the historical person of the prophet isn't even 100% verified).
There seems to be two distinct types of books. The islamist side which doesn't mind giving itself away by adding "PBUH" every time the prophet's name is mentioned, and the opposing side which may or may not have an other agenda but draws different conclusions.
The interesting thing is though, they seem to be using the same unreliable sources while coming to these completely opposing conclusions.
There are some studies which try to find actual historical material to even consider that Mohammad might not have been a real historical person, or that the Koran might have had its sources in much earlier documents etc. These views seem to be accepted as fringe and not accepted by the majority of the historians.
Is it really possible that the Arab world at that time was so completely oral driven that we might never have any reliable material from that period? How about other cultures that interacted with them? Am I being drawn in by fringe theorists that ignore other evidence without my knowledge? Any books/documentaries that might provide more info?
As you say it's a huge historiographical problem.
The side you call "Islamist" is usually referred to as the "traditionalists" because it also includes non-Muslim westerners who nonetheless use the traditional sources extensively. Pretty much all western historians writing prior to the 1970's would fall into this category, although some of the specialists in the 19th century recognized that there were huge problems with the traditional sources. Today the traditionalists often provide the caveat that "Well, we're not entirely sure about this, but the traditional story is..." etc. Montgomery Watt would be a prominent example of that kind of historian.
The second group are the scholars who posit that there are so many problems with the oral transmission of early Islamic history, that there are so many contradictions with the documentary evidence we have that it must be entirely rejected, and we have to try and form a history of Islam from what early documentary sources we have or from non-Islamic contemporary sources. Patricia Crone pretty much started this movement, although as I said there are elements of recognition to these facts in some of the earlier scholarship.
In terms of consensus there is broad consensus that Muhammad was, A: a real person who led a religious community at Medina (the constitution of Medina being an example of a verifiable contemporary documentary source.) B: that the Quran is not a later forgery, although there are debates about whether verses were added, subtracted, or altered when Uthman compiled it.
In terms of definites going beyond that is difficult because it requires reliance on either Sira (biographical literature) or Hadith (the collected statements of the prophet.) Internally within Islam these, and particularly hadith, were recognized as being problematic from the start, so "hadith science" developed to classify the soundness of a given report. The result of that science are the current six "sound" books of Sunni hadith. Western scholars that accept hadith in broad principle usually take the purging much, much further, along certain lines. So for example a complicated hadith is more likely to be a later creation than a simpler version of the same report. etc.
There's a great summary of the issue and of the history of the issue here in an essay by Robert Hoyland entitled "Writing the Biography of the Prophet Muhammad: Problems and Solutions" which pretty much covers what I've just written but in much greater detail, and with better examples, and it's only 17 pages.
It's not just difficult to write about the religion of muslims. It's difficult to write about religions in general. With Jesus you also have a wide range of theories starting with people subscribing completely to the canonical scriptures of the church and ending with people who deny the very existence of Jesus. Most academics believe these days that Jesus existed because it's mostly church historians who even care about Jesus. In Islam the biographies of the prophet (peace be upon him is not necessarily used by Islamists, just as it's not just the Christian Fundamentalists who call Jesus "Christ" rather than "Yeshua the carpenter") have never been holy or canonical and oftentimes contained the unsavoury factoids as well. They are called the "Sirat Rasul Allah (may he be praised!)". Of course the latter day biographies got oftentimes mixed with folkish legends and the demands of religious dogma but the scholars have by now boiled it down to several original biographies recorded in the eight century like f.e. that written by Al-Tabari who was footing on now-lost testimonies and interviewed some people who knew people who knew Mohammed (pbuh) in person. The state of scholarship here is much better than in the christian case.
Needless to say what's good enough for a scholar may get religious Muslims angry - think f.e. of the satanic verses.