You should be able to use that guide with a 1.1.1 iPhone if you start on step 7. All you need to do first is run the tiff expoit via Safari (by visiting Link removed, website no longer available -- don't go here unless you want to jailbreak!).
Also, that guide doesn't say to close iTunes at step 7. Unless there is some reason, such as iPHUC needing it, I would close iTunes. The symlink that is used as part of the jailbreaking process confuses iTunes and if it's open it can add additional Media folders to the iPhone.
Speaking of the symlink, this guide doesn't get into it but you will need to remove it for normal syncing. I assume if you keep following the links they will eventually get to it (maybe after BSD). When you get to that part it will look like this:
mv /var/root/Media.old /var/root/Media
The process to do this after using the tiff exploit is a little different:
mv /var/root/Mediaold /var/root/Media
As you can see the only difference is the "." in Media.old.