How can I control this (i.e., allow 'exec' on my USB drive(s))?
either:
mount /media/usb -o remount,exec
or more preferable, add exec into the /etc/fstab entry for your usb drive (you might have to create one). It'll look something like:
/media/usb /dev/sdb1 vfat exec,user 0 0
/media/usb is the point you will mount to, and /dev/sdb1 is the actual usb device. vfat is the filesystem type, and may be something else if you've formatted the stick; but if it's an actual hard drive, it could be something like ntfs. "man fstab" has a list of all the filesystems.
"user" will let non-root mount it.