My only regret is that I cannot really create a Muslim style religion, since there is no 1 God in the Tolkien world.
Actually, that's not entirely accurate, Aslan. Eru, or Illuvatar, is the one God of Middle-earth. The Valar, while often mistaken for Gods, are more akin to angels, with them acting as the guardians of Middle-earth and the servants and companions of Eru.
You might want to take a look at the Silmarillion for further clarification, as well as various entries in the History of Middle-earth volumes.
In any event, even if you go with the Valar being gods, there's no reason why, just because the people of Northwestern Middle-earth follow this belief that all the peoples of Middle-earth have to. Maybe they just worship Eru, and ignore the Valar altogether, or perhaps they only revere one of the Valar, or perhaps a Maia who walks among them (a living god, in a sense).
There seems to be lots of possibilities here, depending on what you really want to do, and how much of a role you want religion to play in your chronicle.