What TOF described is exactly what is happening. It will always 'super saturate' somewhat when you are making it because it heats up which aids in more dissolution of the iron. When it cools, voila: precipitate. If the precipitate bothers you, you'll need to filter and decant it probably two to three times over the course of a year to get the majority of it out.
If you are getting a LOT of sludge when it cools, then you're adding too much iron too quickly and it's heating up too much. If you hold you hand against the container when making it, it should only feel mildly warm, never hot. Like Jim mentions, slow it down.
Unless your mix is really, really loaded with sediment, it's won't affect the stain at all.
The sludge has other uses if you filter it out and dehydrate it; the particle size is exceptionally fine and it can be used as a coloring agent in varnishes that will be transparent as opposed to most coarsely-ground pigments that just look muddy in an oil or varnish. You can render oils anywhere from yellowish-orange through reds with the stuff and it's more finely 'ground' than most anything you could buy. All depends upon how you dehydrate it. I'm positive it was used historically.
