Couple of thoughts: The issue with lighting everything on fire and having Mat fight in it is that on the threat scale, the fire part of fire is only the third killer. Smoke kills, and so do collapsing buildings. So let's not be in the middle of a blaze. It's a nice tactic for losing pursuit, but not something I'd want to try long term for a fight.
This plan is beased upon the whole, there are no hinges left, so no gate, right? If there is a gate, the only difference would be that Mat tries to use air step and stealth to open our side first while the Knights charge as soon as she does.
[X] Plan: Hold the Open gates and start a Blaze.
-[X] Make a pair of gates, or bars, or some kind of portable barrier to place into the open Gates once you take them. Make some smaller ones, but that would be able to block dwarven halls in the citadel, if you need strong points.
-[X] Charge the open gate(since no hinges survived) with Knights, with Mat on shadowsteed and Dread Aspect. With dwarves running in behind them. Take and hold the open gates from the other side as fast as possible. Speed is life here, you want to be blocking the other side before anyone gets close.
-[X] Give some Caltrops to the Knights. Both to scatter outside the Gates on the Inner Side, or drop behind them in retreat if this is some kind of trap.
-[X] If time and space allowed, take some torches along. Some Knights can ride down the avenue, just a bit, and throw some torches around to help the blaze start, as well as spread the caltrops. But only within easy withdrawl distance.
-[X] Have archers police the walls and bring in Grudge Throwers right behind the charge. Even before the Citadel falls, the Grudge throwers can throw over the walls and set fire to the caldera shanty town with dwarven incendiaries. That should give pause to any greenskins and flush out any surprises hidden in the buildings. Not even they like walking through literal fire.
-[X] As possible, bring up a couple of bolt throwers and use them to police the approaching avenue and take targets of opportunity while the incendiaries do their job.
-[X] Dial in a couple of cannon on our side of the gates. If something nasty shows up, a pre-set signal should allow them to shoot anything trying to boil out of them from the underways.
--[X] Assuming all goes well, if you hold the gates with Knights and the shantytown is burning, once they dwarves arrive and plug the gate, all that will be left is fighting for the citadel and the underground approaches. And the dwarves know tunnel fighting far better than you do. We can bring archers up as we spread through the Citadel, to hold the walls from without.
--[X] Really, if we manage to hold the Gate and start a blaze, the biggest issue will be smoke and the underways. As well as any reinforcements that might come along the walls themselves. We can help with that by having some cannon on our side, that can sweep the top for enemy reinforcements, but the tunnel fighting is going to hurt if they are ready. Ask if the top of the walls is wide and sturdy enough for a wolf charge, if needed.
I don't think Mat really needs to further risks her neck by going into an unknown goblin/orc shanty town. While scouting would be nice, for once, with a pissed off goblin God hangging around, let's not.
TLDR: Since the gates are open, just charge them at speed with Knights, take and hold them, and bring up grudge throwers to throw over the walls and start a fire. Simple, solves most of the problems we can actually solve and makes anything that could be hiding in town come out in the open. If it's a trap the knights can retreat just as fast. The underways aren't a problem we can actually solve. The rest is details.