Yep---what butcher said, although there should be no need to incinerate, assuming you have washed the gold properly, and rinsed it well. Incineration wouldn't serve much of a purpose for re-refining gold powder.
If you inquart, you start over, removing base metals. By re-dissolving the precipitated and WELL WASHED powder, you have already eliminated the vast majority of the contaminants. Therefore, when you precipitate the re-dissolved gold, there is far less garbage present to be dragged down by the gold. Net result is an improvement in fineness, assuming you practice good shop hygiene and have clean and good work habits. Make sure all of your vessels are very clean, and don't melt in a dirty dish. Make it one that has never been used for anything but PURE gold.
Harold