Make a Diamond-Net out of AmSteel and then Put the net over top the Tarp and have it tied off real tight to solid anchor points around the area. When the branch comes it will most likely get deflected by the AmSteel or at least slowed down enough not to cause severe damage to you. AmSteel is pretty light so it is something that wont hurt you on the weight but it might on the wallet. Making a 8 x 10 net out of the stuff could be quite expensive. Anyways, that is the only thing I could come up with, aside from climbing the tree and cutting down all the branches(out of the question for multiple reasons).
I got this idea from when a widow maker fell in my yard and broke in half over some Amsteel I had left strung between two trees from when I was test hanging my diy tarp. I then realized that it is strong enough to withstand alot of abuse from falling objects. It may not be 100% effective but it will definitely help minimize damage taken from falling branches. Icicles, are another story.