Leather cleaning

Leather lounge suite, 30yo.
The headrests have all got a thick build up of something like wax. It can flake or scrape off and leaves perfectly clean leather underneath. Don't think that is a practical way of cleaning it all though.
I've tried olive oil, olive oil plus vinegar, dishwashing liquid, meths all with no discernible effect. Sard prewash spray seemed to soften but still didn't remove it.
Any other suggestions? I'm thinking turps, cold (so it cracks off) or heat.

(I guess it could either be some sort of hair cream or hair spray.)

My wife just bought a second hand leather lounge. It was Moran so I contacted them re cleaning. We bought a cleaning kit from them ($69) which included a cleaner, a leather conditioner, brush, pen for removing ink, a sponge and a soft cloth
Couldn’t believe the difference - I thought it was clean to start with!

Attachment 463691

Fortunately this set is dark brown, but a good clean probably wouldn't hurt.. I'm just not sure a normal cleaner will remove whatever this is.
Unfortunately, Tessa who made this, closed 1 July - and they were only a few K away.. 😢

Update...
I found an icepack made the wax pretty stiff and allowed it to flake off, but that was pretty slow and I don't think was helping at the thinner edges.
A little turps did work pretty well.