I know where to get fleece, and with a level 70 I can blow through the karakuls like nothing. But I can't seem to get any HQ fleece. I've managed to get about 150 fleece but only 3 of them are HQ. Is there a way to increase the chance of getting HQ items from mob drops?

I was considering putting a set of gathering gear on my RDM or loading up a set of gear with perception materia to see if that helps. Has anyone tried this?