I’m just trying to get some more information from you at this point.
I’m guessing most of the 6 mm is probably from a 5mm piece of wood. Is it plywood or a board or some type of composite like MDF?
Have you tried cutting with the leather side up?
Is the charring on the leather, the wood, or both?
Your problem is because of the different densities and composition of your materials. While its possible you might find some magic combination that works well I don’t know that the odds are in your favor at this point (without knowing more).
I think with a composite piece like this though you’d want to run faster cuts and probably lower power and just make as many passes as needed. Note: everybody has different cutting recommendations and philosophies. Go with whatever works for you.
If all that fails, why not cut the pieces separately and glue them afterwards? No idea what you’re making or why that might not be an option, but then you can at least optimize for each of your materials to get the finish you want.
Good luck and share the finished product if you figure it out (and can).