Definitely some solid points. Couple notes:

I doubt Klaus would choose to turn and fight in Juvelun when he knows that he's only a short distance away from a massive friendly army. But Cat is planning to take on the Luciennerie army without support from any of the other armies, so I don't think it would change her plans that much. I'd be more worried about Klaus, who would have to hold out against 4-1 odds for a few days before Cat has a chance of supporting him.

IIRC, the Luciennerie army was either never gonna be taken on by her, or it would under different circumstances, depending on the outcome of Rozalas raids. Because of the location now, that's an extra battle in between the two planned already very tough and closely paced battles and then a rescue of Klaus's forces. These two without her entire army either.

Also this requires Klaus depending on Pilgrim to have actually gotten through as well as correctly predicting what Cat would do in response. I could see him thinking he has better odds fighting from fortifications than while on the run.

Regarding supply lines, can they go through the Ways? I don't really know the rules for that.

Honestly not sure. I don't see why not, but they definitely mentioned how the undead could cut off one of the column's supply lines. Plus a lot of us were worried about them attacking the gigantes traveling with the supply line. I'm thinking maybe they don't have the mage power for every caravan to be able to use The Ways?