Device is Mounting as Read Only (Can Copy Files as Root)

Figured it out (thanks to everybody who helped jog the brain a little bit).

Because usbmount is doing the automounting, this is where the problem lay. And, conveniently enough, usbmount provides a configuration file for managing how a drive gets mounted. In order to manage this, open /etc/usbmount/usbmount.conf.

There is a line in the file that looks like this:

FS_MOUNTOPTIONS=""

Add the uid and/or the gid that you would like the device to mount as.

FS_MOUNTOPTIONS="uid=1000,gid=1000"

Now, my drives automount correctly every single time.

The accepted answer does not work for me (Ubuntu 12.04)

However modifying /etc/usbmount/usbmount.conf and changing the line starting with MOUNTOPTIONS, adding ,uid=1000,gid=1000, did the trick for me.