Yes, I finally figured it out. I found my saves in /title/00010000, but also in another directory, for Mario Kart.
All saves are located in title in a folder xxxxxxxx/yyyyyyyy/data. I copied all files under data to a directory called savegames on my sd card, under a folder named xxxxxxxxyyyyyyyy. I then used SaveManager from Waninkoko after having played the game once to restore the saves.
For the miis, the process was a little more involved. The Mii database is /shared/menu/FaceLib/RFL_DB.dat. I used an hex editor to extract each mii to a separate .mii file. I used the page
Wiimote/Mii Data on Wiibrew to correctly split the file. The mii files were imported after with Mii Installer.
However, the Miis imported that way cannot be edited since they were created on another console. The fix I did for that was to 0x1C through 0x1F in each Mii to the same bytes in a Mii I created on the new wii, and then extracted with Mii Extractor.
Everything works quite well now, except online stuff, but it doesn't bother me much, I wasn't playing online enough anyway. So, if someone else follows those steps, be aware that not all online stuff will be transfered. (I had my Mario Kart stats, but they seemed incomplete).
Next step will be to unbrick the other wii, I'll order the infectus soon, and probably post some pictures (it's a recent Wii, maybe bushing will find it helpful).
Thanks for your help metroid_maniac!