I think i can help you with this question, the best places for take this bestiary is on tiquanda jungle and Liberty bay.
Its true that all respawns of parrots are extremly little!
But here u have a little tip for this kind of bestiary, when monsters have less than 100hp u can farm it with fire bombs in rapid respawn!
You only have to search the exact point where it respawns (its easy, just cover all area with fire bombs, they have super low hp and they will die in the exactly sqm they appear), cover it with fire and mark it on map.
After this, u have diferents marks on your map where parrots appear, u can use this tip too with all little montsers,
In rapid respawn u can get aprox 10 monsters/minute/sqm with fire.
Its not insane way to make it, but u can do it while u take a shower or u are dinning,
I hope i helped you