Except that the destruction of the essence is said to both result from and cause the death of the Warden it was trapped in. The way the ritual surmounts that problem is by sidestepping it, not by correcting it after the fact. If you think Morrigan is lying, fine, but if she's giving the Warden anything like the truth, it's too late once the Warden dies.
I am uncertain how this is relevant to the point we're disputing.
If the explanation we are given for why this works is anything close to true, there is nothing to snag after the Warden's soul is fried. Furthermore, that same explanation also precludes doing the ritual with a non-Warden to any effect whatsoever.
The problem is that if Morrigan's explanation is correct, that wiggle room pretty much vanishes if the Warden pulls a US.
Well firstly, IIRC the explanation of the US comes from Riordan, not Morrigan. And any in-setting 'facts' about what happens at that moment can probably be viewed as after-the-fact conjecture at best. After all the 'Grey Warden kills Archdemon' scenario has only happened four times before over the course of history and never in an environment that allows for observation and study of the event. The Wardens likely just saw a dead Warden and no new Archdemon forming, then took an educated guess from there.
So really, the destruction of the Archdemon's essence is not the solid fact you're presenting it as. For all we know, the Archdemon essences are never destroyed, just rendered somehow unable to posess a darkspawn and create a new body for itself in a process that is fatal to the Warden involved. Pehaps they are always purified of the darkspawn taint and go to wherever dead OG essences go.
And once the essence destruction is established as *not* being an ironclad fact, it's not that hard to imagine a way of getting the OG soul without saving the Warden.