The article I pointed to does not consider the effect of introduced animals on agricultural production.  

I can't answer your question, but it might be important to consider that agricultural produce from the sweet potato fields supported the largest pig herds in the eighteenth century Pacific.  The Hawaiian farmer at that time figured out how to balance human and animal consumption.  I think it is plausible that a workable balance could be figured out today, but I don't know how it might be achieved.