I have backups of some games that I’d like to launch from the Home Menu instead of going into USBLoader GX. I’m also hoping to have these games run entirely off the Wii console, without an SD card. Is something like that even possible?

I think what you mean is that you can install games onto the NAND, but only WiiWare and Virtual Console games for that matter. If you want more storage, then an SD card with at least 8GB is all you need.I don't think you can install Wii games directly to the NAND, and even if you could, the Wii NAND is only 512MB and 200~ are already taken by the OS, IOSes, channels, save datas, etc.
The closest thing you can do is create forwarder channels for your games with WiiGSC.