While your rejection of 'eternal generation' or 'eternal procession' conflicts more directly with other aspects of the Nicene creed, it also conflicts with the consubstantiality of the Father and the Son. For example:
"Consubstantiality" describes the relationship among the Divine persons of the Christian Trinity and connotes that God the Father, God the Son, and God the Holy Spirit are "of one being" in that the Son is "generated" ("born" or "begotten") "before all ages" or "eternally" of the Father's own being, from which the Spirit also eternally "proceeds."
But you have rejected the connotation.
Setting such a connotation aside, I don't see how you can consistently affirm consubstatntiatlity and reject eternal procession. The idea that the Father and Son share an essence that is numerically one and simple (i.e. not just two things with identical properties) seems in conflict with the idea that three persons can have that essence of themselves.
So what do you make of passages like Eph 1:3?
1. I don’t regard Wikipedia as the gold standard of theological discourse.
2. ”Consubstantial” simply means “of one and the same substance or essence” (OED).
3. At a minimum, the purpose of the homoousios clause was to exclude the notion that the Son is merely of “like essence” with the Father, rather than identical essence.
4. From what I’ve read, there’s a scholarly dispute over the more specialized question of whether homoousios was also meant to denote generic identity or numeric identity.
5. You confuse the semantic question of what the word or concept means with philosophical question of how the Trinitarian persons can be consubstantial. That’s not a semantic question. Rather, that’s a question for philosophical theology. A Christian can affirm the consubstantiality of the Trinitarian persons without having to endorse any particular explanation.
6. I don’t have to explain how the Trinitarian persons are consubstantial to affirm their consubstantiality. I certainly don’t require a philosophical explanation or justification for my affirmation. Rather, it’s sufficient for me to affirm their consubstantiality in case I have exegetical warrant for the full divinity of the Father, Son, and Spirit.
7. Sexual metaphors like “generation” as well as kinematic metaphors like “procession,” don’t begin to explain the way in which the persons of the Godhead are consubstantial.
i) For one thing, a metaphor is, by definition, figurative rather than literal.
ii) For another thing, a metaphor posits an analogy between one thing and another.
iii) Apropos (i-ii), you need to delimit the intended scope of the metaphor to isolate and identify the literal comparison.
8. How do you decipher these metaphors? Do you think they stand for a source of origin and/or mode of origin? Do you think the Father caused the Son and the Spirit to be?
If so, then that reduces the Son and the Spirit to the level of a creature. It also suggests some form of pantheism, like Neoplatonic emanationism. Or else it treats the Son and the Spirit as contingent beings whom the Father wills into being.
That’s a self-defeating way to affirm the full divinity of the Son and the Spirit.
9. If your objective is to preserve numerical identity of the Father and Son, then “generation” undermines your objective since what is begotten shares the same specific nature as the begetter, but not the same numerical nature. Both the begetter and the begotten are property-instances of a generic quality. They concretely exemplify an abstract exemplar, which stands over and above them.
If you’re going to make an exception in the case of the Trinity, then that betrays the inherent limitations of the metaphor. And you need to show why your exception isn’t an ad hoc restriction on the controlling metaphor.
10. The Bible doesn’t explain how the Trinitarian persons are consubstantial. And I doubt we could even grasp the explanation.
11. The best that philosophical theology can do is to offer analogies. And that can be useful as far as it goes. But even in that respect, we can come up with better analogies than generation and procession to illustrate the consubstantiality of the Trinitarian persons. As I’ve said in the past, I think the principle of symmetry is a better analogy.
12. Your effort to contrast two things that share an essence which is numerically one and simple over against two things with identical properties is decidedly unclear. For if two things share identical properties, then they are really one thing rather than two, according to Leibniz’ law (i.e. the identity of indiscernibles).
13. I don’t think the Trinitarian persons have the same essence “of themselves,” as if each person is the “source” of his own essence (if that’s what you mean), for sourcehood is inapplicable to a divine mode of subsistence.
14. Since you seem to think Eph 1:3 is in tension with my position, it’s up to you to spell out why you deem that to be so.