I’m not too worried about what term we call it. If you want to stay strictly biblical and stick with Jesus only as the Second Adam, that’s fine, as long as we don’t miss the intermediate typological steps with Noah and Abraham.
I don’t see this necessary myself at the moment (though I would sill use “special creation” with respect to Adam, de novo or whatever), but you already saw how I was ambivalent to the necessity of the virgin birth (though I do believe in it).
Jesus is THE seed of Abraham (and THE seed of the woman) and THE son of David. So, again, as long as we maintain the typology and Jesus as the climactic fulfillment of each.
I don’t have a problem with Noah as a (not THE) second Adam, at least to a degree. The flood is an anit-creation clearly, and God renews with Noah the creation mandate given in Gen 1 (but the 'adam vs. Adam might confuse this connection). And, both have their “falls”; but, yes, Adam’s fall had more far-ranging effects.
So I can respect trying to tighten up the language if one prefers.