How little evidence of Mohammed & early Islam is there?

Eh, I think it is quite clear that there was a religious impetus behind the conquests, though other factors played a role as well. There is a paucity of sources, but we do have them. We shouldn't throw away all the sources from centuries later either. Instead, I think it is better to synthesise all the evidence we have, rather than to stick dogmatically to an ultra-sceptical position or to the traditional narrative of the Prophet's life. The Qur'an for example can be seen as a reasonably early source. I think it's from the 630s, others say c.650, a minority thinks that it dates to the late seventh century, but even if we favour a very late date we can still use it to gain an insight into early Islam. The New Cambridge History of Islam I (2010) sums up this position quite well, arguing that based on the Qur'an Muhammad's time in Mecca can be summed up in this fashion:

The Qur'an itself makes plain that many Meccans quite naturally took him to be a magician, soothsayer or otherwise possessed. There were other reasons to find Muhammad objectionable. As a ‘warner’ in the tradition of early prophets, he emphasised man’s accountability to God, His power, the rewards of Heaven and the punishment of Hell. He also levelled criticism against the prevailing social norms, railing against female infanticide and the abuses of wealth. None of this apparently sat well with the polytheist establishment, especially because he came to attack its gods and claim the Ka'ba for the One God. As his followers grew in number and Muhammad grew in stature, the opposition to his movement stiffened.

This new narrative lacks detail, but that's pretty standard when writing histories of the late-antique world. We can definitely supplement this with later sources, as shown in this article by Andreas Görke, a proponent of using later sources to extract information on the earlier period. However, even he acknowledged that there are limits. He has spent quite a long time working on traditions derived from ʿUrwa b. al-Zubayr, resulting in this summary of the Prophet's time in Mecca:

Based on the traditions of ʿUrwa b. al-Zubayr, for instance, only the following facts relating to the time before the hijra may probably be considered historical: when Muḥammad starts receiving revelations from God, he is at first frightened and distressed, but then starts to proclaim the message he receives. At first, the Meccans’ reactions range from being unconcerned to showing sympathy. This changes when Muḥammad begins to preach against their gods. Subsequently the Muslims are harassed and some of them emigrate to Abyssinia. The situation in Mecca at best ameliorates a little for a short while and thus Muslims begin to emigrate to Medina. Finally Muḥammad follows them together with Abū Bakr and settles in Medina.

This is of course largely similar to the vague story we can extract from the Qur'an, except in this case we can add a few names to the story as well. There is definitely room for further exploration though, since the huge corpus of later Muslim sources are by no means fully analysed yet, so keep watching this space, especially as there are still significant debates over the basic chronology of early Islam, such as over the year in which Muhammad died, a dispute usefully outlined by Chase Robinson here; this extract alone should give you a sense of how uncertain historians are about this:

Eleven alternative accounts [...] have it that Muḥammad was alive at the time of the conquest of Palestine. Since these events can be securely dated to 634 or 635, his death in 632 is obviously thrown into some doubt. The earliest is a Greek text composed in about 634; thereupon follow a Hebrew source written between 635 and 645, a Syriac account from about 660, several more Syriac texts from the later seventh and eighth centuries, a Coptic account (translated from a now-lost original Arabic), one in Latin (written in 741), a piece of Samaritan Arabic and, finally, a document that is conventionally known as ʿUmar’s letter to Leo, which survives in eighth-century Armenian. It is a pretty good haul of evidence: Greek, Hebrew, Syriac, Armenian, Latin, and Coptic sources, written by Christians and Jews of multiple confessions and orientations, who were composing in a wide variety of literary genres, for varying audiences, in Spain, North Africa, Egypt, Palestine, Syria, Northern Mesopotamia and south-west Iran. [...] It seems to me that the burden of proof now lies with those who would defend 632.

The other contemporary source is the Constitution of Medina, which is seen by most scholars as a genuine document detailing the rules governing Muhammad's fledgling community in Medina. It is true that outside of this and the Qur'an we have no contemporary sources talking about early Islam, but that's not unexpected - we have no literary sources from this region before this period, nor were outsiders particularly interested in talking Arabs doing things in the Hejaz. Rome and Persia were engaged in the 'last great war of antiquity', an epic struggle between the two great powers that lasted for 25 years. Even for this well-known event, we only have a few good sources - a Greek chronicle more interested in calculating the date, a Greek panegyric praising the emperor Heraclius, and an Armenian history from the 660s are the best we have. Contemporary Persian sources unfortunately did not survive, though some probably survived into later medieval traditions, but then we have to question whether they preserve genuine unaltered historical facts from the seventh century or if they had evolved in the mean-time. As the Arab conquests picked up pace, the Roman sources decreased in quantity and quality as well - the Greek chronicle-writing tradition stopped around 630 and would only be picked up again in the ninth century.

We have a range of early non-Greek sources though, but they all have issues. The most useful are a late seventh-century Coptic history that skipped everything between 610 and 640, an Armenian history with limited geographical coverage and a bunch of fragmentary Syriac chronicles. There are also a lot of letters/sermons from churchmen that sometimes mention the Arabs in an off-hand way, but nothing that provides a detailed narrative. I wrote a survey of these early sources here, so I won't go into too much detail here, but it seems reasonable to say that the Arabs had a religious motivation based on the clues provided (though as before, treat these ideas only as suggestions!).

The main problem, as I see it, is in collecting all these sources together and then using them to write a coherent story. This, as you can imagine, is a very difficult task, but it is entirely possible. I think Holland went too far in his interpretation and I highly recommend you to check out Fred Donner's Muhammad and the Believers: At the Origins of Islam (2010) and Robert Hoyland's In God's Path: The Arab Conquests and the Creation of an Islamic Empire (2015); the first provides an interesting thesis about Muhammad's time in Arabia, one that I found very convincing, whilst the latter is a very up-to-date overview of the Arab conquests. Both are meant for the general public, so they are just as readable as Holland's book. Of course, these books will only give you some historians' interpretation of events, so don't think that everything is settled yet or trust them completely. I'm sure more revisions and controversies will happen before a 'definitive' narrative of this enigmatic period can be written. For the evidence themselves, Hoyland collected basically all the literary evidence in his Seeing Islam As Others Saw It: A Survey and Evaluation of Christian, Jewish and Zoroastrian Writings on Early Islam (1997), so it's a very convenient resource that you can check out if you are interested.