@SylvainFontaineJive I've had this solved for quite some time now.
First, apply two patches to libstirshaken:
https://github.com/signalwire/libstirshaken/pull/124 https://github.com/signalwire/libstirshaken/pull/125
Then apply my PR that @henningw linked.
https://github.com/kamailio/kamailio/pull/3289
Then you should be all set. Feel free to share your feedback to those PRs if it works for you.