Punky wood absorbs moisture very quickly and I find it dries slowly because it's wet inside.
Right, and if you happen to be burning pine that was standing dead, or slab cuts, you quickly discover punkiness is a matter of degree: certainly pine that is cut green and burned the next year will not be at all punky, but pine that is a few years dead is definitely prone to reabsorb moisture even though it doesn't seem to appear that punky.
I don't need to perform any experiments with a moisture meter because I have performed them with my stove. Older mill slabs and standing dead eastern white pine burn great if covered after being split, but sometimes not so great if not covered.