Amadaun, you do make a good case and I admittedly do have more respect for the angle you are taking than the one I am concerned most people take.
The traditional approach that was applied to various polytheistic gods is valid. I believe, however, that the reason this is possible with those gods is that the understanding of gods in those particular cultures was inclusive. There was room for understanding those gods under different names and forms because they represented universal forces of nature and the psyche. Local understanding of those forces might differ from place to place but that to which they correspond can be said to be the same.
The conceptions of God which arise out of Judaism, Christianity, and Islam, however, are a bit different. Each religion claims a direct line to a God who is said to be the exclusive ruler of the universe. Understandings from outside the religion are held to be erroneous from the outset by virtue of the notion that all truth has been revealed to the believers. The stories overlap because each group grew out of the group which preceded it.
One must note, however, that each group distinctly rejects the other groups' understanding of the nature of deity. Muslims believe, for example, that their God revealed himself to Jews and Christians. They also believe, however, that Jews and Christians are guilty of shirk and in danger of hellfire for their erroneous beliefs. Christians likewise believe that God revealed himself to the Jews but also believe that they err grievously for rejecting Christ and the Trinity.
I don't know; I could be wrong. It's just that when I see three mutually exclusive understandings of a deity that openly reject one another in substance, it's hard for me to say that they all follow the same God. There are too many contradictions which must otherwise be reconciled for their mythologies to truly be combined into one, at least for me.
EDIT: I should add that, in my mind, combining the three into one God would necessitate a principle to which they would correspond. There is one such principle I can think of -- that of the demiurge, as the type of God espoused by those three religions fits the bill for such a being perfectly.
Pointing that out, however, does not go over particularly well when trying to convince Christians that they worship the same God as Muslims!