You are correct that conventional tactics are not likely to work, which is why Tramennis is far more likely to use asymmetric tactics, which is far more viable with GK 'storming the castle.' Small units CAN effectively engage larger units, with the dual outcomes of a) slowing down an advance, as additional measures must be taken to secure the column, and b) inflicting casualties.
Think of a team of soldiers clearing a building in an Iraqi/Afghani city: It takes a decent sized team to enter, clear and secure a building. Even one or two enemies can make that process considerably more difficult and time-consuming. The entry team cannot advance without ensuring that each room, each closet, each stairwell, each and every potential hiding spot is cleared. Tramennis can use this absolute necessity to his advantage.
Edit: The larger the building (in this case a huge tower), the more troops and more time are required to conduct the sweep. From what we have seen of the interior of the Tower, it will take GK forces a significant amount of time to clear each room and corridor on each floor.
The difference here is that a team of soldiers clearing a building in an Iraqi city have an interest in keeping the building, and the city, intact. GK does not. Now that their purples and reds are on the ground, they can level the whole city building by building, never having to waste time or units in clearing out buildings when they can simply pulverize the Garrison from the inside out.