I am working on making the Rescue Remix boot from usb stick. Here is the procedure for Ubuntu:
https://help.ubuntu.com/community/Installation/FromUSBStick

And this is what I have gotten working for the Rescue Remix:

1- Make the USB flash drive bootable using SYSLINUX.
sudo apt-get install syslinux
syslinux -s /dev/sda1 (assuming the device is sda1 - Use the correct device name!)

2- Obtain the Ubuntu-Rescue-Remix disk (or just mount the iso as a loop filesystem) and copy the contents of the CD to your flash drive (make sure you include hidden files/directories).

3- Copy some files from sub-directories to the root directory.
Copy all the contents of isolinux to the root directory of the usb drive. Do the same for Casper.

4- Rename the file isolinux.cfg to syslinux.cfg and edit it a bit.
Change /casper/vmlinuz to /vmlinuz and /casper/initrd.gz to /initrd.gz in both (all) stanzas.

5- Boot the computer from your USB flash drive.

I will refine this in the near future. Any suggestions are welcome.