I've been throught exactly the same process as you. And what I have found works better than anything else is to slip a cheap foam sleep mat in 'between the double layer of the hammock. I widened mine by cutting up a second sleep mat and adding "wings" on the the mat, thus making it as wide as the hammock. Well worth a try, and much less weight than using a sleeping bag as insulation.
I was lying out in my hammock in the garden last night, minus 5 degrees, looking at the starry sky for a couple of hours, with only a wool blanket over me (I had my indoor clothes on) and my back and bottom were toasty warm against the hammock/foam pad layer and only slightly cool on top!