Hello everyone! I have tried all of your suggestions and finally have good news!
First of all, I prepared the files on my SD card: cIOS d2x installer to install d2x v10 beta 52 with base 58 on slot 251 (it wasn't available for download on ModMii), Wiiflow Lite and the WAD for the latest version of the original MIOS (v10) that I got from NUS Downloader. I checked the hash of all my Wii backups on Wii Backup Manager (MD5 hash, that is) and all of them came out green, so I'm assuming they are all okay. I also checked that all of my backus are PAL. Finally, I deleted the controllers folder and ninconfig.ini from my SD and also the ninconfig.ini file in the root of my GCN USB device, and copied the "games" folder from my USB device into my SD card with the Pokémon XD backup for testing purposes.
Then on my Wii first of all I installed the original MIOS with YAWMM and d2x v10 beta 52 with base 58 on slot 251 from the cIOS d2x Installer app. Both successful. I proceeded to launch my original copy of Mario Kart Double Dash!! from the disk channel and it worked! However, when booting the same disk from Nintendont I was getting the "No Signal" screen after loading the games as if I had unplugged the Wii from the TV. GC backups stored in my USB drive were giving the same result. I attempted to load the Pokémon XD backup I had moved to my SD card, but I got exactly the same result.
I moved on to testing my Wii backups. WIthout any new changes in configuration, the situation on USB Loader GX was exactly the same as before, and same results on Wiiflow. I changed Loader IOS to IOS 58 and Game's IOS to IOS 251 on USB Loader GX and all of my Wii games started working!
During testing I also noticed that Pokemon XD was showing up on USB Loader GX (my other GC games don't), so I decided to load it from there in case something would change. And boy did it change something! Pokémon XD Gale of Darkness loaded perfectly! I went back to Nintendont and loaded the MKDD disk, Pokemon XD from my SD card and all of my USB drive backups one by one and all of them worked perfectly, except for Mario Party 7, which is still giving me a black screen right after booting up. I suppose the updates I installed just needed time to replicate and sink in.
So, current situation: All my Wii games seem to be working flawlessly so far, I will keep testing and see if I get a freeze at some point. All GameCube games are working perfectly as well, with the exception of Mario Party 7, which is still giving me a black screen.