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But the question remains and I do not yet see an answer that is plain and clear

I think you just answered it yourself. You allowed that the Jews worship and adore the same God as you profess to worship and adore, albeit not with the full understanding of the truth. I believe you. The common factor is each of these three religious traditions professes to worship and adore the God of Abraham. All three also believe Isaac and Jacob were blessed and chosen of God. There is only one God of Abraham, Isaac, and Jacob. The Messiah went to the Samaritans who also professed to worship the same God of Abraham as the Jews. The Samaritans were in error, yet they had a common reference point to the same God.

That's interesting but I think you are wrong.

I thought we were talking about the Muslim God of today. Did Mohammed receive inspiration (when he wrote the Quran) from the same God that the Holy Roman Catholic Church worships? No. Although Ishmael was the progenitor of the Arab people, Muhammad did not (after 610 AD at least) worship the same God as the Jews.

Today's Muslim is worshipping a different god from the one that Hagar trusted and believed. Their perspective, their understanding, their concept of God has changed. Allah is a significantly different from the God that the Jews and I worship in truth. The Jews knowledge of God is incomplete. The Muslim God is a complete distortion of the God of Abraham.

Their distortion is so great that it is not the same God I serve

Now, I understand your view. I understand your perspective. I don't agree with you.

We've had an interesting discussion and I sincerely thank you.

In a related note, I want to present a prophesy about Ishmael that has been fulfilled.
He shall be a wild donkey of a man, his hand against everyone and everyone's hand against him, and he shall dwell over against all his kinsmen.

After laying out in my previous post to you what was in my mind, I found this confirmation (fwiw), which describes my belief on the question at hand ("Are they the same God?):

The Origin of Islam: The "Previous Scriptures"
The origin of Islam is controversial. The "previous scriptures" mentioned above are the Hebrew Torah, the Psalms of David, and the Gospels of Jesus Christ (Sura 4:163; 5:44-48). The Qur'an accepts these books as divinely inspired and even encourages us to test its claims by these "previous scriptures." "If you have any doubt regarding what is revealed to you from your Lord, then ask those who read the previous scripture" (Sura 10:94). But this is where we run into a problem. The problem is that the Qur'an thoroughly contradicts the Torah, the Psalms, and the Gospels. For example, the Qur'an explicitly denies Jesus Christ's crucifixion (Sura 4:157-158) while all four Gospel accounts clearly portray Jesus Christ as crucified and resurrected.

SOURCE

There's more there to see, but if I copy too much you may not read it.

On a personal note: I know you and I have great differences. You have been very gracious in this dialog. Thank you.