OK, mixed some of the dryest gunk with acetone and ran it through some filter paper. These are the results ...

Gunk as it scraped off the J cloth after filtering out bio/water. It was scraped from the top of the filter where it was the dryest. It had the consistency of a paste.

Gunk with a few mls. of acetone added ... no real effect immediately.

After mixing, it appeared to form a suspension ... nothing seemed to dissolve.

Filtering arrangement.

What was caught in the filter.

Acetone after filtering. Not too obvious from the photo, but it didn't appear to be discoloured. The Brown tint is very fine particles which passed through the filter paper (Not lab quality paper. Just paper from a commercial veg oil filtering system).
I ran methanol through the original Jcloth filter and pretty much the same happened. I've just been down and checked what ended up in the filter paper after an afternoon of drying and it's like a very fine, still sticky powder binding together.
Don't know if any of that helps?