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.

I often braid round a thin core of jute when I'm using wool. Removes any stretch and gives it a bit of hardness.

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

I boiled the wool and then stretched it. It made the sling longer and somewhat less elastic

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.

It begins with wool selection before braiding. Select a worsted yarn, with high twist. So a dense and firm yarn, nothing fluffy. Examples are rug yarn, sock yarn or tapestry yarn. Coarser hairs in the wool can also help.
While braiding use a lot tension.
I'm not a fan of treating a braid after it was made. It's better to start with the proper material and to work accordingly.