WOW: Just realised that you're running LE 7.0.2 - is there any reason why you haven't upgraded?
I've replicated your setup (Albeit on 8.2.5) of 3 partitions. (2 LE) and one NTFS and everything worked as expected - /dev/mmcblk3 was mounted as RW at /var/media/NTFS and I could read,write and delete. So something seems to be happening at the Windoze level.
Do you really need to manually use the SD card to transfer data when SFTP or Samba will do the job over the network?