Ah in that case, I see. But doesn't change the math of possible troop numbers.
They didn't have any other army to stop Kittiya there besides unarmed ~270. So they asked Grey Order to help and they did a very long run to help (Kittiya got attacked right above Haen, look on the map where it is).
And your math is inaccurate.
1) Not all of them started in the first day, I'd say it's more like 50-60% did that.
2) Most of them didn't start recruiting from the first day
3) Some of them don't recruit even now
So their maximum army was not more than 1/4 of what you said.