Thanks for the report. I'll try to take a look at this if I get time, but I can't really promise when I'll have time or whether I'll find anything. As the progress report described, debugging an issue that only happens during online play is rather difficult.
If you want to take a shot at it, the best starting point is to try to determine if making certain instructions fall back to the interpreter fixes the issue. If you enable Dolphin's debugger, there will be a menu in the menu bar that lets you disable entire categories of instructions. (Disabling too many at once will make the game lag!) Falling back individual instructions requires editing Dolphin's source code.
If you want to take a shot at it, the best starting point is to try to determine if making certain instructions fall back to the interpreter fixes the issue. If you enable Dolphin's debugger, there will be a menu in the menu bar that lets you disable entire categories of instructions. (Disabling too many at once will make the game lag!) Falling back individual instructions requires editing Dolphin's source code.