Actually, there are quite a few errors in your statement.
It is a fact that Mohammad was born an al Hashim of the bani al Quraish and it is a fact that the Hashim did control the Kaaba and that Abu Lahab did insult Mohammad when he performed the tawaf around the Kaaba while the Statues of al Lah, al Lat, al Uzza and al Mannat were still there. There were no 360 Gods there, just 4.
Mohammad was not a Prophet then and he hadn't even met Waraqa bin Nofal.
However, after he became the Prophet and after he returned to Mecca after the Battle of al Bad'r, he did remove the statues from the Kaaba.
However, the story that he destroyed all of them, which was made to make him look like Abraham who destroyed the idols that his father made to sell and feed the family, which the Sahaba and Caliph Uthman wrote may not have been entirely true.
The reason why the Ummayad Caliph Yasid attacked Mecca and destroyed the Kaaba was that he was sure that Mohammad had hidden the statues in the basement and that many of the Meccans were still idolaters.
Anyways, the word al Lah was the Arabic word for the God, and it was used for the idol of Hubal as well.
It doesn't mean that the Muslims continue to worship the old idol which is long since destroyed.
Do the Muslims unwittingly follow the rituals of the old Cult?
Yes.
The Kaaba was the Temple of Hubal and the tawaf, walking widdershins or anti-clockwise around the Kaaba was the old ritual which Mohammad revived. He also revered the al Hajarul Aswad, or the Kaaba Stone and revived the pilgrimage in it's name. And, he changed the qiblah to the Kaaba from Jerusalem. He also lied about the miraculous Zamzam spring being a well near Mecca knowing fully well that the real one was in Beersheba in the Negev Desert of present day Israel.
Do the Muslims know that these things are true?
No. They will never accept it because they've got blind faith in the words of Mohammad and they do not study the History of the Jews with an open mind.
However, the fact is that they believe that they worship the God of Abraham and not anything else.
While they are wrong, I wouldn't blame them because that is what they are conditioned to believe.
Now, I know that I'll be called an Islamophobe and even an Orientalist [because I respect the Hindus and the proto -Hindu Faiths which I find make a lot of sense], but denying History doesn't make it go away.
What Mohammad did was right for him and his people. He needed to give the Arabs who were descendants of Ishmael who were second rate in comparison to the Jews the feeling of supremacy to have them rally around him. So, he did it. He re-wrote History claiming they were the Words of God by simply changing everything and claiming - God said so.
But, that doesn't change facts one little bit.
It only makes the Muslims get the tunnel vision that becomes their reality.
If they would study their own Faith more deeply, they would see all the inconsistencies and know how much of it was all made up by one man and how much they had to cover up for all that.
But then, most of them would start leaving that fold, so, it's not allowed to them and they will only see what they are told to as the Truth.
The most ridiculous thing about the Muslims is that most of them are Ajam, or don't speak Arabic; neither do they belong to the Arab Race where only the Adnani Arabs were the descendants of the Jews who were of the 12 Tribes of Ishmael, and these people like to claim that they are also from the lineage of Ishmael, when in fact, they are not even close to that. Even the Wahabi Kings of Saudi Arabia are non-Adnani because they belong to the lineage of the relatives of Amina binti Wahab who was a pagan and a non-Adnani Arab.
But then, they say "Ignorance is Bliss", don't they?