Hello bwood, Well this is a question I've not come across before, hopefully one of our TA's here will see your question and offer some info.
Better yet, you should ask your own travel agent if trading cabins can ever be asked of those other passengers ahead of time. Because if this can be handled before sailing day, your TA is, of course the person who will have to deal with it for you. Don't even bother to try to deal with it yourself through the cruise line (I mean calling from home) because the cruise line will not deal with you directly if you have a travel agent.
If you don't have a TA and have booked directly, well then definitely call the cruise line and ask as soon as possible.
Either way, it will never hurt to ask. What's the worst that can happen? ...they say "no". Well in that case you're no worse off than you are now.
And if the TA/ or cruise line does say no, ask if a trade like that can be made while on the ship, if your cabin neighbors are willing to go along with it. Better to know now if they can't do that, so that you won't get your hopes up.
One note, if your only choice is to ask the neighbors to trade, after you are on the ship, I suggest you do your best to be on that ship as early as possible, so as to catch the neighbors as they enter their cabin. I think it would be really imposing on the neighbors to ask them to move if they have already started unpacking.
Also, take a really good look at the deck plans. Is there anything special about that cabin that the neighbors have? And is there any negative quality about the one you'd be offering them? I don't think it would be right to expect them to accept a lesser cabin than what they had booked.
It may be something very minor that would make it a lesser cabin to them. Such as having an upper birth in the proffered cabin. I personally avoid those cabins, as they give the room a closed in feel. It may not seem like a negative factor to you but, to someone who's a little claustrophobic wouldn't want that room. And on the opposite side of that situation, maybe their room has the third birth and they need it.
Also, I avoid cabins that connect to another cabin. Those cabins may only have a small chair instead of a love seat, or a little love seat instead of a sofa, to accomodate the door.
And for all you know they may have their kids booked in the room directly across the hall from them, and won't want to be any farther from them than that.
Whatever the situation, be prepared as there are many reasons you may get a "no" answer.
Good luck, and be sure to let us know what the TA says.