This makes no sense. A typical Wii softmod doesn't touch the system menu, any of the standard IOSes, the games themselves, or anything really other than installing HBC, the cIOS which only gets used by homebrew, and placing homebrew on the SD card. None of that should be able to affect the running of legitimate games, it's resident in the system but otherwise leaves the system completely unmodified and does not do anything unless launched, that is unless you install something like cIOSCORP or DarkCorp, which does overwrite the standard IOSes with a cIOS, which might lock the drive speed to 3x instead of the standard 6x if it forces the drive into DVD read mode, although I have never seen complaints about slowdowns across the board from doing so, it would only be in specific circumstances or specific games. Or install Priiloader which does patch things that could potentially cause issues, but nothing like this.
I have a feeling the slowdown is not related to the softmod at all. Maybe the optical drive is going bad, or just needs cleaning?
Can you tell us exactly what you installed or what guide you followed? Was it anything beyond the usual HBC, cIOS, USB loader setup?