The problem is that the exchange APIs do not allow for withdrawing funds if I'm not mistaken, so all the transfers between the exchanges would have to be done manually. Or am I missing something?
At this point this is true. If automated transfer were to be negotiated with the exchanges, the bot could make the transfers. If not a simple re-charge routine ("send x number of LTC to x address") could make "recharging" a one click process.