I'm kind of at my wit's end here. I've scoured everywhere I could possibly presume to online and nobody has reported a problem similar to this one.
I'm including details I forgot to mention in case it might help isolate the cause of this issue. I'm using mattguitarist's Mod 2 for WiiSX Beta 2.1 with Hermes' cIOS202, on a WD Elements USB 3.0/2.0 1 TB Portable HDD (all relevant WiiSX files are on this, as with all emulators I use: there is no cross-use with an SD card), on an NTSC Wii on 4.3, with the appropriate BIOS and .CUE/.BIN game files. I am positive everything is up-to-date. I have tested these game files and the BIOS file on other emulators to ensure they aren't the problem. This problem is exclusive to WiiSX (analog sticks on any controller Not64 registers work perfectly in it), is consistent across all games (I am not making the mistake of setting the input to analog for early PSX games that don't support it) and controllers, across all possible settings changes, across at least 2 WiiSX versions (I tried Mod 3 just to ensure it wasn't an odd one-off) and is the only problem the emulator has. Everything except this specific issue works perfectly. The specificity involved makes me reasonably confident the problem isn't caused by anything outside of WiiSX (whatever massive volume of possibility that might represent), as I would presume were that the case, the issue would be more widespread, but of course I can't be certain. I am at a loss and it's a shame because analog controls are next to integral for many PSX games.
If anyone could shed any light at all I would really appreciate it. This is an excellent emulator and it's frustrating such an apparently obscure problem is nipping it in the bud for me.