I got it to work. For the record:
I moved all the files (fmodex.dll, GMFMODSimple.dll, GSWBINfile.dll, readme.txt) everything except the game executable app, data folder, and savedata folder. Then have the patch launcher point to the folder that only contains the game executable app, data folder, and savedata folder. Then re-add the fmodex.dll, GMFMODSimple.dll, etc back into the game folder after patching is complete.
I did not know that the patcher needs to interact with the game executable app and datafolder. Anything else inside the folder will interfere with the patcher app.