Having come across Amsteel and the site
L-36.com, I discovered there are lots of instructions for various ways of making halyards using Amsteel (which is made from Dyneema).
I found one that shows how to splice 3/16" Amsteel to a leader made from cheap double-braided rope. I used that to make both a jib halyard and a main halyard, where the portion that runs from the cleat on the mast to the sail is made from Amsteel, but the part that you pull on while raising the sail is made from double braid 1/4" or 5/16".
The double-braid is much grippier, but also cheaper, and unlike the part of the halyard that goes up the mast when the sail is set, the "tail" does not contribute to weight aloft or windage. The instructions were fun to follow, except that the suggested size ratios on
L-36.com did not want to work for me. For one of the halyards, I used a much thinner tail, for the other, I used a length of 5/16" Amsteel as an intermediate. Splicing that to either the double braid or the 3/16" Amsteel was no problem.
I finished the ends of the halyards differently. For the Jib, I terminated it in a soft shackle. I tied a small loop with a bulky knot to the head of the jib with a "luggage tag" knot (cow hitch), and that's what the soft shackle loop on the halyard end grips onto. Works fine.
(The two ends would be tied into a bulky knot, e.g. a diamond knot).
For the main, I originally did an eye-splice to continue to use the SS shackle I had been using with the previous halyard. After a few seasons I noticed that the shackle was preventing me from raising the main all the way. It cost me almost 2" of hoist.
I found a way to make a luggage tag knot with the end of the halyard through the cringle on the head of the main -- without needing to remove the thimble and eyesplice, even though they didn't fit through the cringle. I've sailed a season with that setup and it seems to work well, if a bit non-conventional. (I'm leaving it as a challenge to the reader how to make that knot).