You might try some sunguard thread.
http://www.yourautotrim.com/pusuthch.html It is for sewing stuff exposed to the elements. I've never see it fail in 20 years. It would need a size 18 needle. An old clone or Singer 15 with the tension set for the heavy thread might be a good machine for it unless you are going through a LOT of layers. My old walking foot machine (Singer 111) had a horizontal bobbin so I doubt if it really matters if the tension is set right. But it might be easier to set the tension on a vertical bobbin case.