I think I'd split by bedroom, so 500, 250, 250, though I can see a case for person 3 paying less since the bathrooms are shared. So maybe 550, 250, 200, or 500, 300, 200, or something along those lines, makes sense, too. Personally, I think wanting to pay even less than 1/4 because I have to share a bathroom seems a little petty. If I wasn't wanting to be part of a big happy group, I wouldn't go on vacation with two families with kids.
As a single person, I would be perfectly happy with splitting it by bedroom. (As a side note, overall, I'm not sure renting a 2 bath place for 8 people is ideal, especially depending on the age of the kids.) I do think that maybe talking about the bathroom schedule ahead of time might help. (Some people are probably going to need to shower at night, for example. Who is willing to do that?)
I also agree that just having the conversation and showing you are open to opinions will probably make everyone happy. Since you are willing to pay for half, I'd start out by saying something like, "Hey guys, we should probably talk about how we are going to pay for the cabin. My initial thought was that we split the cost by room, but I'm definitely open to other splits, especially given the bathroom sharing.[I'd add that part to make it a little easier for the single person to suggest a different split if they want to.] Anyone have any thoughts?"