Would the performance difference between 10 and 20% free be that big?
Free space unformatted isn't bad necessarily. I don't need more space. I just want to make it faster.
Hard to put a number on it, but yes, drives slow as they fill. The outer tracks are fastest, primarily because of the speed which they pass under the head; fuller it gets, slower it goes. The big slowdown comes at the point in which there are not enough contiguous blocks to write out files in sequential space: disk fragmentation.
I would always shoot for at least 10% free space, but to maximize performance and (to a lesser degree) reliability, 20%+ free is better. For max speed, 50% free is better, although you may have a performance bottleneck other places, like the controller itself.
Free space on another partition could help with not using the inner most tracks of the drive if the second/free partition is last on the drive, but it will not with the fragmentation issue once the volume is mostly full.
Best bet would be to write everything out to a safe backup, and create a new, larger array. One nice perk of moving files: all files will be defragmented doing the move, assuming there is enough space to write out everything.
If you don't have enough space on a single volume, you could move the file off in chucks on multiple drives. Clunky, but it would work. Reverse the process to write data back to a new array volume.