Yes, there is. This link gives the new one, which is common and showed up ~1975. Here' one link, that shows what I should have seen, but saw the "new" version instead. The use of the word eternal is irrational, the use of "before all worlds" is not. Jesus was more than just capacity, which is all "eternal generation" could refer to. Generation is an action, which requires that it occur in time. The earliest time it could logically happen is by decision after the first ponderings of creation. There would be no logical reason to "generate" one's person, before they pondered doing so.
"Arius's "there was when the Son was not" is heresy. "
I don't know much at all about what Arius said, or the details. What I do know is that Arius claimed Jesus was a creation, which is wrong. Here's a link to what Arius said. "the Arian, though he did not come straight down from the Gnostic, pursued a line of argument and taught a view which the speculations of the Gnostic had made familiar. He described the Son as a second, or inferior God, standing midway between the First Cause and creatures;" This doen't even resemble what I said.
"And no, God does not need to exist in time. Time is a created thing."
Time in this world is a created thing. Time in God's Heaven is not created, nor is it the same thing. In order to exist at all, time is required. In order to use the word "eternal", time is required. In order to create, time is required. Just because no one can read God's clock does not mean it's not running.
"Any appeal to physics is appealing to created things, which only by an improper analogy have any application to theology per se."
If God is real, then their must be an underlying physics. It was known in the OT, that no one could see the Father, or they would die. That's, because of the physics. The Church fathers refer to the physics of God as "substance". If there's no substance, then there's nothing. The physics of this world are not to be mistaken as the physics of heaven. The physics of this world are represented by the cherubim waiving the flaming sword in Gen 3.
"Physics may have some relevance to economy, but not to theology. "
Physics has no relevance to economics, other than the intellectual conception and the phenomenas studied rely on the underlying physics to exist at all. The "physics" is the reality, not the math. The physics refers to the "substance", it's nature and interactions. The math applies to both. In the case of physics, it is physical theory. The theory is not the physics, it represents the physics.
God, as usually described transcends physics. Hence metaphysics.
In order to exist at all, time is required.
True for finite, changing, material existence. Not true for infinite, non-material. In theology, 'eternal' means "existing outside all relations of time; not subject to change."
You are making basic category errors in addition to gross reductionism.
You seem to have argued yourself into the Arian heresy by over-reliance on created physical categories. For your salvation's sake repent.
The Acta of the Ecumenical Councils and histories of the Arian controversy are readily available. Read them!
And learn the terms of art before arguing theology: economy, as in the phrase 'God's economy of salvation' like the other use of the word is derived from a Greek word meaning the management of a household, and refers to God's dealings with the world, rather than that which is proper to Him alone, which is the subject of theology proper.
As to 'new versions' of the Creed--they are forbidden by the Third Ecumenical Council. Modification to the Creed is the most salient reason for the schism of the Latin church. At least the adjective 'eternal' applied to the begetting of the Son is true, unlike the second procession of the Holy Spirit, but there is no authority to put it into the Creed. Nonetheless, there is no new Creed.