Maimonides did call him a madman. See the translation of his Epistle to Yemen here (3rd paragraph) or here on Sefaria (search for "madman").
To summarize the historical background (brought here)
About the year 1168, the Jews of Yemen were confronted with a three-pronged agonizing problem. A fanatical Moslem cleric became
the ruler of this distant, primitive South Arabian land and decreed
that his Jewish subjects convert to Islam under the threat of harsh
punishment and suffering.
Their agony was compounded by a Jewish
apostate who embraced Mohammedanism. To demonstrate his zeal for his
newly adopted faith, he began preaching to the Jewish communities that
Mohammed was a divinely sent prophet alluded to in the Bible and that
Islam was a new, divinely revealed religion superseding Judaism.
Hence, the apostate argued, the Jews should yield to the ruler's
demand and embrace Mohammedanism. [...] Rabbi Jacob al-Fayumi turned
to Rambam for advice and counsel.
Rabbi Moshe ben Maimon [Maimonides] addressed a letter to this sage,
and through him to the entire Jewish population of Yemen. He states
that the root of all anti-Semitism throughout the ages is envy of the
Jews being the Chosen People and the recipients of the G‑d given
Torah. Unable to do battle with the Almighty Himself, the haters turn
their jealous rage toward His people.
Throughout the ages this has taken three forms [...] [3.] the false claims
of new religions - Christianity and Islam - that Judaism is no longer
valid and Jews must be forced to accept the new revelation. He
consoled them by telling them that the Jews are a unique and
indestructible nation; that all the past and present sufferings and
persecutions were foretold by the Prophets, and just as in the past
the nations had failed to annihilate the Jewish people or destroy the
Jewish religion, so will the present persecution fail, and peace and
tranquility will return to the community.
He contemptuously dismissed and disproved the assertion that Judaism has been supplanted by Islam and showed that the claim that Mohammed
is alluded to in the Bible is based upon nonsensical interpretations
recognized as such even by the Moslems themselves.
Rambam advised that the self-proclaimed Messiah is nothing but an impostor and no doubt a madman. He urged them to remain firm in the
belief that G‑d will send the true Moshiach to redeem the Jewish
people from suffering in exile at the proper time.
The epistle accomplished its purpose - the Yemenite Jews remained
faithful to their religion in the face of their bitter suffering.
Rabbi Moshe ben Maimon used his influence at the court of Saladin in
Egypt to intervene in their behalf, and the persecution came to an
As noted in your original source, in his compendium of Jewish Law (Mishne Torah Melachim 11:4), Maimonides wrote that Jesus and Muhamad served to prepare the way for the true Messiah by turning people to monotheists.
Ultimately, all the deeds of Jesus of Nazareth and that Ishmaelite who
arose after him will only serve to prepare the way for Mashiach's
coming and the improvement of the entire world, motivating the nations
to serve God together