Perhaps it is not real Islam. Someone should ask Chaim about this. I heard once it can be considered a separate religion like The Druze which also was originally a part of Islam.
It is also argumentable that a majority of "Muslims" aren't real Muslims just because they don't believe in the part of The Koran that says to kill all the infidels. Islam is not like Judaism. A Jew is born a Jew no matter what they believe in, even if they convert to another religion. But a Muslim is not a Muslim if they don't believe in The Koran, just like Christians are Christians just by virtue of believing in Jesus. In Judaism, you are religious by doing the mitzvot. Believing isn't enough. If you believe but don't do all the mitzvot, then you are just Traditional. But in Islam and Christianity, believing is what makes someone religious and in the case of Islam, not believing makes someone no longer be a Muslim. Perhaps a Christian here can say if someone can stop being a Christian by not believing. I know someone who likes JTF and he agrees with Chaim's position on the definition of a Muslim. But by that, he believes a majority of Muslims aren't really Muslims.
From what I have read of Islam, and from what I know of my own religion (I'm a christian if you don't already know), I don't agree with all your points here.
From what I have read of Islam, someone who is born of muslim parents is considered to be a muslim, if they then reject Islam, they are often treated as is suggested in the quran:
"Those who reject Islam must be killed. If they turn back, take them and kill them wherever you find them". Surah 4, verse 89.
Regarding my own religion, if you do not beleive, you are not a christian, sinmple as that, some people would call themselves chrisitian despite not beleiving in Jesus's sacrifice, or even beleiving in God at all, however, that is just like saying you are computer programmer who has never seen a computer, it makes no sense. Christianity is not a race, it is a set of beliefs, it is the belief that Jesus, God's son, and at the same time, part of God, died to save us from our sins, someone who does not believe that cannot be a christian.