Modding it would definitely help. However, the Wii should be able to read save files from an SD card. Did you check to see if the save was recognized in the Data menu (or whatever it is called)? You might just need to copy it over.
The only other thing to try would be to create a save on the wii, move it to the SD card, then replace the Monado0x files with the files from Dolphin.
Edit: If for whatever reason you want to try using a .bin file, there is a tool created specifically for Xenoblade to pack a .bin. Just follow the readme and change SX4P01 to SX4E01.
The only other thing to try would be to create a save on the wii, move it to the SD card, then replace the Monado0x files with the files from Dolphin.
Edit: If for whatever reason you want to try using a .bin file, there is a tool created specifically for Xenoblade to pack a .bin. Just follow the readme and change SX4P01 to SX4E01.