The easiest solution is going to be to install Ubuntu 6.10 as directed in the instructions.
You can see from the error log that the LinuxMCE installer is hard coded to look for the edgy updates. There are what it is going to check against. It also updates specific packages to satisfy dependency issues for additional packages installed from the LinuxMCE CD.
Your choices are to edit the numerous entries in multiple files that hard code updates, version numbers and web locations...or simple follow the directions and install Ubuntu 6.10.
I have tried it both ways...the RTFM / FTFD method is far, FAR easier and faster too.
Long and short: Yes you can get LinuxMCE to install on Ubuntu 7.04...or you can take the easy way out and use Ununtu 6.10. Knowing what I know now...I'd take the easy way everytime.