It wasn't Mohammed who founded Islam.

[Rayaan]

Sounds reasonable, yes... up to the point where Sebeos, an Armenian bishop, writes, around the 660's, about Mahmet, the preacher. Remember that guy?
I still wonder why you presented him as an example of someone mentioning prophethood for Mahmet.
I can understand the name morphing due to different accents and writing on consonants, but the absence of prophethood in the text you quoted... it's strange....

I doubt that your reading comprehension is really that bad. But, if even if that's the case, I'll quote the entire thing and explain it to you.

At that time a certain man from along those same sons of Ismael, whose name was Mahmet [i.e., Muḥammad], a merchant, as if by God's command appeared to them as a preacher [and] the path of truth. He taught them to recognize the God of Abraham, especially because he was learnt and informed in the history of Moses. Now because the command was from on high, at a single order they all came together in unity of religion. Abandoning their vain cults, they turned to the living God who had appeared to their father Abraham. So, Mahmet legislated for them: not to eat carrion, not to drink wine, not to speak falsely, and not to engage in fornication. He said: 'With an oath God promised this land to Abraham and his seed after him for ever. And he brought about as he promised during that time while he loved Ismael. But now you are the sons of Abraham and God is accomplishing his promise to Abraham and his seed for you. Love sincerely only the God of Abraham, and go and seize the land which God gave to your father Abraham. No one will be able to resist you in battle, because God is with you."

When you have lines like, "Now because the command was from on high, at a single order they all came together in unity of religion," this would most reasonably resemble the role of a Prophet and not just a preacher. The passage seems to talk about a decisive moment when people were "abandoning their vain cults" and started to unite themselves by turning to the God of Abraham, which perfectly conforms with the Muslim tradition of the Prophet Muhammad, who is believed to be a merchant who was divinely inspired and urged everyone in to abandon their idolatry and paganistic belief systems and return back to the monotheistic faith of Abraham.

In the same quote we also find the line:
"So, Mahmet legislated for them: not to eat carrion, not to drink wine, not to speak falsely, and not to engage in fornication."

These are the exact things which Islam prohibits as mentioned in the Quran:
Prohibits carrion
Prohibits wine/intoxicants
Prohibits false speech
Prohibits fornication

Also, Sebeos mentioned that Mahmet was a merchant, and Muslim tradition has recorded that the Prophet Muhammad was a merchant too:

Wikipedia: "The Islamic prophet Muhammad was born and lived in Mecca for the first 52 years of his life (570–622). Orphaned early in life, he became known as a prominent merchant, and as an impartial and trustworthy arbiter of disputes. He married his first wife, the 40-year-old widow Khadijah bint Khuwaylid at age of 25. He would not take other wives during her lifetime."

and raises suspicions about the later claims made in the qur'an and hadiths.

Not really, because there is nothing in it which contradicts the later claims made in the Quran and hadiths, is there? Rather, if anything, it matches up with the later claims, as I just proved above. The preacher's name and the details that follow have more in correspondence with the Islamic description of Prophet Muhammad than anyone else. Thus, the preacher, merchant, and Prophet mentioned in the passage above is most likely to be a reference to the Prophet Muhammad, because the details in it are perfectly compatible with the Muslim view.

What we know and can attest to (Sebeos) is that the rumor of Mahmet's leadership seems to have reached the outskirts of the arab reach before the rumor of his prophethood, hinting at different origins for both these rumors.

Well, there's a 50 percent chance that either of those claims/rumors would be written down before the other one, so the mentioning of his leadership before his prophethood doesn't really mean anything significant.

Secondly, all the quotes in that link which hint at Muhammad's leadership do not in any way negate nor discredit the his role as a Prophet, either. Leadership and prophethood are not antithetical attributes. Why? Because the concept of "Prophet" - as Muslims understand it - already encompasses the idea of leadership when it comes to both religious as well as political affairs. The Quran and hadiths, in many places, mention the battles that took place and how Muhammad was conducting the plans and actions as a leader of the Muslim army. Therefore, even the quotes in that link which convey the existence of a military leader named Muhammad confer credence to our present understanding of the man's life. So the quotes there and the Muslim traditions about who Muhammad was are in full harmony.

Later evidence by itself is not suggestive of a later insertion, especially if the early and later claims are consistently the same. If Muhammad's prophethood was a later insertion, then most likely there would have been some discrepancies between the earliest claims (like the ones in that link) and the later claims about him (the hadiths), but yet there is none.

Here is something else ... the earliest reference of Muhammad from that link:

... and in January, they took the word for their lives (did) [the sons of] Emesa [i.e., Ḥimṣ)], and many villages were ruined with killing by [the Arabs of] Muḥammad and a great number of people were killed and captives [were taken] from Galilee as far as Bēth [...] and those Arabs pitched camp beside [Damascus?] [...] and we saw everywhe[re...] and o[l]ive oil which they brought and them. And on the t[wenty six]th of May went S[ac[ella]rius]... cattle [...] [...] from the vicinity of Emesa and the Romans chased them [...] and on the tenth [of August] the Romans fled from the vicinity of Damascus [...] many [people] some 10,000. And at the turn [of the ye]ar the Romans came; and on the twentieth of August in the year n[ine hundred and forty-]seven there gathered in Gabitha [...] the Romans and great many people were ki[lled of] [the R]omans, [s]ome fifty thousand [...]

... which, once again, lends more credence to the later accounts of what happened, specifically regarding the battles in Emesa and Damascus.

And these are not just from Muslim sources only.