Since I hammock in an urban park, and have opted to take a convenient, but easily accessible place, I have had to think of a way to hide my bag while I sleep. (I try to leave it inside locked places overnight, but for certain reasons this is not always possible).
I use a HH+SS. At first I would put the bag in the UnderCover. However, this only worked when I didn't actually need the UC, and anyways, I ended up thinking that it might damage it.
One solution: design an UC -- it could be a under-under-cover -- that is designed to put things inside and, perhaps, that can be sealed (though I concluded that, as long as it looks unified with the hammock, it may not be recognised for what it is).
Then, I began taking the left-over rope after tying the hammock to the tree, tying it to my bag, and then bag to my main knot on the rop. This effectively held my bag at the far end of the hammock and out of my way (I hate sleeping with a bag just laying around in the hammock). This works well enough if the bag isn't too large, but it stops me from fully zipping the hammock, and it may disturb the shape of the hammock and, by consequence, harm both durability and comfort.
Another solution, not yet tried, is to take a waterproof bag and lift it up inside a tree, and then tie that to my hammock in a way that means that the whole hammock will have to be untied if the bag is to be lowered. I'm not too fond of this solution since it makes the contents inaccessible, though I can see how this might work in some situations.