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Okay, I figured it out.
>Change to battle form
>Give Korai/Mirai the item you want to dupe
>Go back into ride mode, this saves the item
>Change them back into battle mode
>Perform the bug as described in the thread. If you did it properly you'll be asked to where you want to put the item (just send it to the bag) and will deposit Korai/Mirai
>Press start to respawn Korai/Mirai. Change into battle form
>They'll be holding whatever you gave them earlier, and another will be in your bag from the one you sent earlier
It would seem the ride mons are saved differently from other Pokemon, probably as a fail safe so pressing start probably just loads the previous state they were in.