I use Bob's method by wetting thoroughly, letting it return to tooling status, bagging it and then refrigerate overnight (at least). Most of my projects lately have been big enough to not be able to finish in one sitting, so I had to come up with something. I Know the fridge keeps the mold away too because I was fighting with that for a while and now I don't have any. Also, since my items are so large, I wrap them up in GOOD cling wrap in sections then stick it all in a garbage bag before putting it in the fridge. I find that with that method, all I have to do is unwrap the portion I'll be working on, spray the backside with a little water then get to work. When I take a break, I re-wrap. Basically from the time I cut out the leather until I'm ready to dye it stays wrapped in plastic to maintain a constant moisture level.
All that said, I've never felt that my work feels any stiffer or anything after it's finished. But, I don't use any oil or conditioners until I'm done tooling so there may be some validity to that part of it.