Amsteel for a tether is a bad idea. You can't friction hitch to it effectively, you can't mate it with an ascender safely, and trees can wear it out quickly. Amsteel is still unproven as far as climbing applications go. To be on the safe side, just stick with climbing rated equipment for your life support. If you want to go lighter and more compact, go with oplux.
@DanO sells oplux by the foot now on double steps.com