Why aren't you saying THIS IS THE ONE TRUE GOD? The god you pray to says he is:
Deuteronomy 4:35 & 39
Deuteronomy 32:39
II Kings 5:15
Isaiah 37:16 & 20
Mark 12:29-34
John 17:3
1st Timothy 2:5
It seems like you're trying to hedge your bet - you acknowledge that there's a significant flaw in the myth of your god, so you leave room in your worldview that "god" may not be who you think he is.
It's actually a very Roman view, whether you know it or not. The Romans prayed to an "unknown god," because they acknowledged they may not know everything about every god, so they hedged their bet by sacrificing to this unnamed god, "just in case."
I guess that conveniently gets you off the hook of the "where you were born dictates what god you pray to" if you can somehow wrap your brain around the God of the Bible being one & the same with Allah - even though he explicitly states he isn't, and he isn't ambiguous about who he is.
It's like marrying a woman but feeling free to sleep with every other woman on the planet because it's possible they all share the same soul. You can try that if you get caught sleeping around, but I doubt your wife will be on board with it.