I use mineral spirits as solvent for greasy parts. Let the black solution sit in a clear soda bottle, and the sludge settles to the bottom in a day or three. Then, pour off the clean stuff off the top and you are ready for reuse.
That said, I'm not sure if the same separation will occur with that "goo" you have dissolved. It's worth a try, though.
BTW, maybe just me, but I've never had any luck filtering anything other than coffee with a coffee filter.