Right after I got mine I oiled all over with a light coat of hydrophane, then subsequent heavier coats on the flaps (not knee rolls and not seat). Not saying that’s necessarily the right approach, but I’m very pleased with the result. I did the same thing with the first one that is still going strong at 18 years old, so I don’t think it will hurt anything.
I think a little oil will speed up the break-in process and help it soften. Mine isn’t fully broken in yet b/c I’m 8 months pregnant, but it is well on the way after a dozen rides. My old Stoneleigh fits like a glove, can’t wait until the new one does too – it just has a bit of that slick new grain leather feel still, though the balance is superb.