We’ve covered this here: Would God's Guidance Be DNA-Detectable?. Given what we know of population genetics, a priori we do not expect it would be detectable, even if we allowed every selectable mutation to have been inspired by God.
In principle, I agree with you. However, in practice, the immense amount of effort invested in arguing against common descent speaks something different with DI’s actions.
You basically have it it right, though I wouldn’t say “incontrovertable.” Remember, I have also made the case for a de novo Adam. Rather, I’d say it is very clear that God made us in a way that we looks like we share common ancestry with the great apes.
Given the evidence, the only viable argument against CD have to engage with theology. Not finding any contradiction between CD and Scripture, even if see teaching of a de novo Adam, there are no theological grounds for rejecting common descent. It looks like we share common descent with the apes, because we in fact did. Of course, I’m open to hearing other arguments, and I am happy to legitimize people taking different views, as long as they don’t justify themselves with anti-scientific arguments.
As for scientific evidence alone? The evidence, at most, could suggest God’s involvement. However, as I explained, we do not expect this would be detectable a prior. God could have been clear in the evidence. Imagine a world where humans-chimps had very different genomes, and archaic humans (e.g. Neanderthals) did not exist. Such a would would very much trouble or even disprove an evolutionary interpretation. That, however, is not the world we find. Instead, we see gobs of evidence that suggest common descent that need not exist unless we really did share ancestry with the apes.
That, in my view, is part of why the Genealogical Adam is so important. It makes space for the traditional account in the evolutionary story. It takes back ground that was lot. That should change the calculus for everyone.