Similar problems
I am having similar issues though my Drobo is about 80% free space 5TB out of 6.
My iTunes library is there and I also use it for my Time Machine backups. As a result, whenever time machine is doing its thing (every hour) iTunes becomes almost unusable. Just scrolling through the list of apps to select/deselect on my phone becomes excruciating as every scrolling movement on the magic mouse results in a 20 sec beachball.
Apple TV seems to play fine regardless.
As to time machine, the last hourly backup (of about 58MB of data) took more than 20 min - so one third of the hour before the next one.
This is getting rediculous..
