This approach uses the Intel Compute Stick's 64-bit bootloader and official Canonical software. It supersedes my earlier approaches.
Download the 64-bit Ubuntu 14.04 ISO from http://releases.ubuntu.com/trusty/ and write to a USB using 'Rufus' on Windows or 'dd' on Linux
Plug the USB into the device and power-up and use F2 to change the bootloader to 64-bit (i.e. Ubuntu 14.04)
Now use F10 to boot from the USB and install Ubuntu. You will now have a bootable Ubuntu but without bluetooth, wifi and sound
Reboot into Ubuntu and download 'linuxium-z3725f-patch.sh' from https://drive.google.com/file/d/0B99O3A0dDe67endsMWtBT3k5ZUE
Open a terminal window and make the file executable (chmod 700 linuxium-z3725f-patch.sh) and execute the shell script as root (sudo ./linuxium-z3725f-patch.sh)
This will build and install all the required drivers for Ubuntu
Once finished reboot your device to enable a fully functional Ubuntu
Anyone wanting to try the unofficial "official" Ubuntu can use my new Ubuntu 14.04 LTS (64-bit) LiveCD which includes wifi so those "under the Dome" can easily install Ubuntu without the need for a USB ethernet adapter. Download from https://drive.google.com/file/d/0B99O3A0dDe67blR3NE0ycUQxUkk and write to a USB using either 'Rufus' in Windows or 'dd' in Linux.