Any tips ? I love how durable wool is and how little it is affected by humidity, especially when lanolized, of all materials it has become my favorite. It's perfect for slings, I just want to get rid of the excessive springyness.

That's a great tip JudoP.  I never would have thought of that.

Ideally, you'd want to steam it while it's under tension, perhaps using an iron. That causes the fibres to set at the stretched state.
The way I used to do it for Balearic slings was to twist the yarns many times, and lock that tension in the braid. Stretch was never an issue the short slings I made from it. However, if the sling gets soaked it turns into a noodle, not stretchy but very floppy.