It could work, but then there's the issue that Crono and such visit the dimensional vortex before defeating Lavos. Except that they don't, because it's a New Game +...except that they do, because the Gates are still functional (they close after CT).
Since that's all vaporous, then I think we can go ahead and write our own theory in this case, just for a thematic tie-in. So yeah, I think this is pretty cool. We should put it int he next analysis review.
Except this paradox is somewhat resolved by the ideas discussed in the main DS-analysis thread- that the world in which the dimensional vortices exist is a new, revised dimension, created through the "initial" defeat of Lavos and his ensuing fusion with Schala(the idea of causality across time eras and dimensions is rather paradoxical and seems to resemble a 5-dimensional model- time within time) , which is why the vortices as well as a portal to the Darkness Beyond Time in which this fusion has already begun are present.
I was playing today, and I thought it was interesting, what Glenn says upon encountering the Steel Shade. "Even if you are the real Chrono, we will not allow you to harm ours", indicating that at the very least, the Steel Shade bears a very strong resemblance to the genuine article.