I agree that science isn't the same as religion. But science could provide the foundation of a religion that could unite atheists and theists. That religion would be pantheistic.
You want "God" to be defined clearly, as when you say, "folks have to clarify which God it is that they are (not) interested in. Your words are a bit all over the place, unclear."
But that's close to the mistake I talked about in the article. God is supposed to be "precisely" that about which we can't hope to be precise. God's a transcendent being, nothing concrete or objective or tangible.
There are roughly three positions I'm working with here: mysticism, theism, and pantheism. Mystics understand the esoteric meaning of "God," whereas theists are stuck on the exoteric, literalistic, scientistic one. Theists take God to be a particular being rather than the ground of being. Pantheists can absorb both the transcendent and literal, imminent, concrete aspects of God by ascribing divinity to nature. Nature is near to us and also very far from us since the universe's scale transcends our intuitions.
Your model here seems pantheistic, if you're identifying God with a stage of cosmic evolution. But if it's the same universe that's developing, the limiting of nature's divinity to the early stage would be arbitrary. If God is a kind of energy or protomatter, that's not "God" in the strictly mystical or theistic sense, though. The pantheist has some work to do to convince religious folks to adopt a more science-centered approach to religion. Pantheism is atheistic with regard to the exoteric conceptions of God.
Yet when you say that God couldn't have willed creation from nothing, you seem to be working with a theistic, exoteric, scientistic conception of "God." From the mystic's esoteric conception, God can perform miracles that transcend our comprehension and thus our science and reason, so of course God could will creation from nothing. That conception, however, is confused since the appeal to a will is a personification, which makes the conception half esoteric and half exoteric, or half transcendent and half literal. It's just incoherent, which helps motivate the shift to pantheism.