My FLAC files are stored on ext4, on a RAID10 array of 3xSATA HDDs. So quite a bit faster than your external drive. System is an i7 with 16GiB of RAM (so even several-disc albums fit entirely in disk cache). I put all the cover art, at full/original size, in each file (so adding art can easily double the size of the album).
So, I'd guess that's why you're seeing freezes and I'm not. Plus I'd not really think of Picard not responding the input while obviously writing a file as freezing.
[They're then checked in to a git-annex repository, and sync'd across several machines and backed up to Amazon Cloud Drive]
Well, you already should have a second drive, as a backup!
But anyway, if you can resize the NTFS partition, you could set up LVM in the now-free space, and put ext4 on that. Then copy the files, and then add the NTFS partition to the LVM setup. Then grow the ext4 partition to use the full disk. If you have less than 50% free, you could do this in several steps (shrinking the NTFS and adding another partition each time), but it starts getting more and more ridiculous. Note that the downside is that only Linux will be able to read this.
And of course you should have a backup before trying that.
Even if the performance is the same, ext4 (or btrfs) would give you nice things like longer file names and broader character support.