Savemiifrii skips the system menu and starts the disk that is in the wii's drive. So put a disk in the wii, and then turn it on while holding down all 4 sides of a gamecube controller's dpad. You might have to take the controller apart.
If the indiana pwns save is already on the wii you should be able to use savemiifrii to load the indy game and then do the exploit to load an application.
If the save isn't on the wii already, you don't have a way to get it there, if you have no system menu and no bootmii boot2. You'll have to use the stack smash exploit then.
The stack smash exploit does not involve the system menu at all. It exploits the stage creator in brawl, which means you can load the exploit/hack stage right off the SD card. You can use savemiifrii to start up brawl and then use stack smash to run an application. I don't know of another exploit that doesn't rely on the wii menu. If you don't have brawl maybe someone would lend it to you temporarily.
Whichever exploit you use, load the application I linked to earlier to load bootmii IOS, which I assume you have installed. It can do all the backing up and restoring.
Make sure you don't overwrite the old good backup or the new backup. Make backups of the backups!
The restore will probably take a long time. If the power goes off during it you're probably toast.
After the restore, nothing done after the restore backup was made will be remembered. Saves will be reverted and you won't be able to redownload VC or Wiiware stuff purchased after the restore backup was made.
Since this signature affects old posts, I'm leaving a message here in case anyone searches for my username. This account died in early 2013. I am no longer a fundamentalist.
Don't add to my problems by pretending my past views are still held in the present. I do not have any patience for that. Feel free to ask me what I think now.