Oof. I'm pretty sure the way the wind is blowing is more interesting and would make for a better narrative, HOWEVER, I don't think that voters necessarily get why yet and I want to later down the line say: this was all foreseeable.
So. Look, if we were just kicking this up the chain of command then the assumption is we trust our superiors to make the right decision.
If we are trying to hop the chain of command then that means we trust our own judgement more than we trust that of our superiors'.
That being the case, what is our game plan here? Have momma Cai fix everything? Recall our Liege is CRX, she who loves the Law - in both word and spirit. Recall too that Momma Cai was forged in the fires of Ogodei's attack and that her enmity for the barbarian tribes is probably only eclipsed by her enmity towards those who would frivolously spend the lives of their soldiers in countering that invasion. I find it, hm, likely that either a) she will not be the bastion of rationality about this OR b) she will understand (in a way she understands little else) how much her people hate the barbarian tribes.
Either way it will mean that she will not personally move to fix this. The political cost of seeming to be a light touch on the matter of barbarians will be too high.
So. Who is she going to delegate to help take care of this genius idea?
Chances are high that if she is open to the idea at all, it'll be us. If we trust our judgment so much, put your money where your mouth is.
Now, this might not be how things end up playing, but in the broad strokes, I think it's a plausible assessment.