As a former prof. arborist and a rec. tree climber, I have to re-iterate especially what PuckerFactor said about paracord and also what Bluenose said about a Treeboat.
Here's the science and suggested standards on rope and gear:
First, when life is involved(on rope strength), "A safe working load is commonly defined as 1/10th of the current breaking strength of the rope. For rescue applications per NFPA, it's 1/15th of the breaking strength." (From the book "On Rope" p.29)
So, the suggested minimum or safe working load of the rope should be, for example, on a 9mm rope with a typical breaking strength of 4500lbf (or 20kn), 450lbf (1/10th x 4500lbf)
Or looking at it another way, if the rope is tensioned to 450lbf, which could easlily be done given your weight and other variable factors causing tension in your situation, you would need a rope with a min. breaking strength of 4500lbf (450lbf x 10) = 9mm rope.
For this very example, many many climbers will not go below a 9mm rope because of this minimum safety factor.
Your paracord, even doubled, will not provide this type of strength. (660lb total x 2 = 1320lb total, not per foot).
Other things to think about in your setup:
What is the strength of your hammock material under not only your body load, but with additional load from tree branch flex, wind and just the hung tension?
Until you do the math on these hammock factors, I would suggest using the Treeboat designed for this purpose to handle the loads.
Also, an overhand knot can roll, but more importantly, all knots should be backed up with a stopper knot.
Most recreational tree boaters definitely sleep with their harness on and attached to a safety rope with self belaying capability.
Hope this helps to improve your experience!