I'm in the process of replacing the halyard with Amsteel as well. In this context, check out the website
http://l-36.com.
He describes how to splice a halyard
http://l-36.com/halyard_splice.php
I found the descriptions easy to follow, but, here's the caveat, the dimensions he gives didn't work for me. I hadn't used Sta-Set, but "equivalent" rope from another manufacturer, and it was just a bit too wide, so that it simply wouldn't fit the opening in the Amsteel.
Solution: I used a short length of larger diameter Amsteel to make the splice, and then spliced the Amsteel using a Brummel splice. To be deployed whenever I get to take out the DS this season.