The original support lines on a HH are made from Spectra and I think Air Core is also a type of Spectra.
One thought: I have found that using thinner lines has more of a tendency to "cut" things is comes in contact with. I think HE said something about thin support lines damaging his hammock. I used some really small line to secure my HH top cover when I first made it. I had it tied through a webbing loop and when I pulled it out it actually cut the webbing like a hot knife through butter. If you are tying on to the original HH Spectra you may not have to worry about that.
“Light thinks it travels faster than anything but it is wrong. No matter how fast light travels, it finds the darkness has always got there first, and is waiting for it."