Whether stitched or wrapped, I've always used DAP contact cement...I apply it to the inside of the leather and also the bare wood, let it sit for a bit until it gets tacky and then adhere the two pieces...not sure of your process with the 'sliding' of wet leather? I've used the wet/damp leather process before but you have to be careful, with leather being elastic and shrinking when it dries, it can also tear away from your stitching if you're not careful...hope this helps some, cheers - P1.