Don't the stables start at fair? Our fc used a broom maybe 36 hours ago and the condition is still good with around 5 chocobos in there. As for the brooms if you gather the mats yourself you make 20 at a time so not really an issue considering it only takes 5 bamboo sticks, 1 glazenut and 1 broombush.

How you've put it it would seem you have more chocobos in the stable? More chocobos equals more ahem "waste" which would need cleaning. If that is the case then get everybody using it to pitch in to get the mats needed to make your own.