Sadly I don't know the cause of the problem, but wonder if it could possibly be the fact that there is just a glob of ink in the end of the quill and no air getting to it to cause any sort of flow other than a dumping of the whole glob at once? After all, I've seen some dip pen nibs that were designed with a sort of breather hole or slit.
Edited to show this
YouTube video that I found. It confirms there is a slit on the inside of the quill end for ink flow. Also, there is no mention of curing using heat.