There was an active, rehabbing member named, I think,
@momtok (apparently no longer a member) who recommended folding and 'massaging' the bag when the leather CPR is applied. That would allow the conditioner to get more into the lower layers of the leather. (she had quite a good explanation with better language for why this works). I rehab a lot of bags and I've seen the same stiffness that you mention. The folding and 'massaging' makes a big difference. I will see if I can find the original posts. I saved all of her rehabbing instruction posts but they are on another computer.