I have a 20 GB NTFS volume that I was planning on using for a variety of purposes, including being readable by windows with little effort.

Unfortunately, for some reason, I cannot execute any files on the drive, even after following the answer here (I was able to mount the volume just fine, but the error persists).

How can I fix this?

Output from mount:

/dev/sda1 on / type ext4 (rw,errors=remount-ro)  
proc on /proc type proc (rw,noexec,nosuid,nodev)  
sysfs on /sys type sysfs (rw,noexec,nosuid,nodev)  
none on /sys/fs/cgroup type tmpfs (rw)  
none on /sys/fs/fuse/connections type fusectl (rw)  
none on /sys/kernel/debug type debugfs (rw)  
none on /sys/kernel/security type securityfs (rw)  
udev on /dev type devtmpfs (rw,mode=0755)  
devpts on /dev/pts type devpts (rw,noexec,nosuid,gid=5,mode=0620)  
tmpfs on /run type tmpfs (rw,noexec,nosuid,size=10%,mode=0755)  
none on /run/lock type tmpfs (rw,noexec,nosuid,nodev,size=5242880)  
none on /run/shm type tmpfs (rw,nosuid,nodev)  
none on /run/user type tmpfs (rw,noexec,nosuid,nodev,size=104857600,mode=0755)  
none on /sys/fs/pstore type pstore (rw)  
systemd on /sys/fs/cgroup/systemd type cgroup (rw,noexec,nosuid,nodev,none,name=systemd)  
gvfsd-fuse on /run/user/1000/gvfs type fuse.gvfsd-fuse (rw,nosuid,nodev,user=daniel)