.../...It's not original and I'll eventually replace it... Any ideas how to make it supple enough to work with?
Making it soft is certainly an important step. There are vendors that supply "leather softener" liquids.
Another important preparation of the leather, also when you replace, is to skivvy the leather down towards 0,5mm thickness. Book binders for instance use this technique. Written about before on this Forum.
For your enjoyment, a picture from the M-B production 1968, templates for cutting interior leather (colour Bamboo/Bambus)
/Hans S