I was just thinking: building the ram seems like an uncertain proposition. The idea initially was to build the ram to pull troops to one gate, but the Grey Winds want the least amount of people within fortifications as possible, regardless of position. A few more people for Myra to fend off as she holds the gates open is a much better proposition than having a thousand spears in their fortifications, even if they're initially in the wrong position, entirely protected from cavalry and able to mount counterattacks. I think the ram should be scrapped, honestly.
What would be better is for the penal battalions to scale the walls all over the place and get off them asap, getting into the city and drawing soldiers out of their fortifications. Myra stays on the walls and holds the gatehouse with her elites, and then once she has opened the gate the lancers pour in and have a much easier fight in the wide streets.
So: plan.
penal troops scale the wall, get into the city and start fucking things up: no civilian casualties, but property destruction will likely be permitted. Guard is drawn out of fortifications to deal with it.
SImultaneously,Myra and her lot climb the walls near the gatehouse, seize and hold the gate open.
Claes and her force wait, once she sees the gates are open the horses dash in, start fucking things up, seize key locations and hopefully quickly force surrender.
Sound good? Sorry for going back on the ram idea, it just seems superfluous and sub-optimal. Any hint of siege would stop forces leaving fortified positions and make escalade much harder all over the wall, despite enemies nucleating forces at the wrong place.