The crazy creek works similiarly to what you are describing. It has a strap from each corner. Each ends two straps go around the tree and the ends "scrunch up" the fabric the strap goes through. I tried tying my head end straps independantly using two tree to see what it would be like. It seemed to take out some of the flex of fabric and wasnt as comfortable as I thought. Made the hammock more flat than I would prefer and ended up changing it back in order to get the comfy curve for the back. Granted it is not designed to be spread out like that, but even with a stick with notches to assist in the spread at that end of the hammock, I didnt like the "lay of the hammock.
i know what you want to work, but i am doubting its physics. if the 6' is the width, and it spreads around a 2' tree (for simplicities sake each side as a 2' tree), then it would just sag in the middle like a bridge. but there would be no "end caps", making it easier to enter, but also to drop items out of. and if you were to find the ideal space, having 4 trees, with enough slack to make it comfortable, there would be a weird depression in the middle. but still mostly a bridge hammock, or one of those backyars net hammocks with the wood beams.
but all that is just the way i see it, nothing gives better results then making it!
Take a 6' x 10' rectangular piece of material. Attach a strap to each corner. Hang it loose, exactly like a normal hammock. Lay in it diagonally, just like a normal hammock. I'm just wondering if the ends would open up more than a normal hammock and reduce shoulder squeeze. Especially if you had a wide tree or 2 trees so that the straps were further apart.
i don't think you could really lay diagonal in something like that, i could be wrong though.
it still sounds like a bridge hammock, just without the end caps or spreader bars, thus relying on the trees for spread.
you wouldnt need to be diagonal, it would be flat.