We might as well speculate about that, since we lack info with which to discuss the short term. So, the base requirements for us would be to cross the defeat the enemy army, cross the river, secure the bridge for the 6th to support us and then assault the city. If I'm going with the somewhat pessimistic theory that each of the 3 corps represents a force of about 10 thousand strong, we need some pretty decisive victories for that (40 thousand compared to our 20 thousand and change). Fortunately, the enemy is also probably planning to cross the river, something that makes capturing them a somewhat possible proposal (any force that is defeated with their back towards a river crossing would have a terrible time). We might have a chance, if we really smash the first corps, have the second corps cross and smash them again, though there comes the issue of our own crossing. It heavily depends on us getting to perform a bunch of defeat in detail battles and winning decisively. This would be followed by the issue of our own crossing, which would also be pretty difficult if there is an enemy on the other side.
If we manage to successfully get north of the river, chances are alright. We would still face tough battles, but as long as we can strike either at Engelsburg or the bridge we can make progress. There are other outside factors, like the exact enemy choices, strength and getting additional armies directed towards our front. I can see a path towards that if things go well. If they don't, there is the possibility of negotiating quartering from Daurstein.
Fair enough, though that depends on their uniform and field tents, as well as the local climate. I don't disagree trying to fix logistics though, reliable shipments of supplies would make planning things easier.