I have been toying with the idea of a split hammock. My idea is a wider than usual gathered end hammock, about 11' by 8', with an adjustable line running under to separate our individual sag points. If the dividing line is run diagonally, perhaps through loops stitched into the hammock to hold it in place, I'm thinking it would give each of us our own pocket right next to each other without crushing us together. The line could be loosened for a traditional single hang. Has anyone seen this solution tried? What tips do you have to make it work?
If you want to sleep in a hammock, go for a South American one, which is bigger than you describe and asks for a different position in it, (in my view a much better position to sleep in.)
Those hammocks come in double, and owing one of those I can say that two people who do not want to cuddle can roll away from each other and will have a bit of space between them. The most I have seen in my hammock was four teens (which were pretty much fully grown,) but they did fill all the space.
If you want to use the European (and North American) kind of hammock, with a spreader bar, with two, you need more than twice the width of a single one. Your idea of using it with a diagonal line makes me think that you and your partner will be toe at nose and nose at toe, and that is asking for accidents.
If you do want to divide a netted hammock, I would go for weaving a line through the material of the hammock. With a solid fabric one, I think, sewing the string to the fabric will keep it where you want it.