Muslims do NOT see Jesus as the Messiah, but as a special Prophet of sort and not as specially Chosen (but important none the less). As far I know, there is some subtile nuance - and clearly NOT Son of God.
This was my understanding of the matter, that he was seen as an important prophet as opposed to the savior of mankind Christianity says he is.
Just to point out none of your Christological titles besides "Son of God" are strictly religious.
There were Messiahs both before and after Jesus, AFAIK both more or less ended up the same way. Messiah is a political rather than religious title.
Likewise, Son of Man, not strictly religious (its used in Ezekiel in a different context), although the reaction regarding this as blasphemous when Jesus referred to Himself as such implies that it was.
And Lord is simply the Greek translation of YHWH used in the Septuagint.
So Mohammed accepting Jesus as Messiah would not necessarily have religious overtones. The Church at the time wasn't split between Rome and Constantinople yet (not officially, anyway), so Mohammed's Christianity can't choose between Orthodoxy and Catholicism.
Although, it can go Nestorian or Eutychian in its affirmation of the person of Christ. Maybe your Mohammedan Christianity can accept the filioque as opposed to the Byzants if and when it comes up. Since the Council of Toledo accepted it as part of the Creed due to it being used in Spain that they were reclaiming from the Arian Vandals.
Thanks for the input. I can only say that the Nestorian path seems a bit unlikely, considering (as far as I know) that OTL Islam placed a fair bit of emphasis on Mary. As for the filioque, I feel that that could go either way. It doesn't seem like a problem that can be solved by looking at Islam's view of the situation, and I can barely understand the controversy in the first place.