Yes, you can do a CWE to seperate the DHC from the APAP.
1. Crush your pills
2.Dissolve your powder into around 50ml of cold water
3.Take a square of fine cloth (Dress shirt or pillowcase will do), wet it, and attach it to the rim of a glass with a rubber band, creating a convex surface for the solution to go
4.Pour your solution into the filter and allow it to filter itself (Usually takes 20 minutes to half an hour). Place it in your fridge if possible, to maintain temperature.
5.Once there are no more drops coming through the filter, carefully remove it and gently squeeze the remaining liquid from the clump of binders/APAP
If you really want to be sure to get out the most APAP/paracetamol as possible, you can repeat steps 3 and 4 with your DHC/water solution.
EDIT: Forgot to answer the last question you had; The sludge on the bottom is probably a little bit of APAP/parecetamol combined with the binder particles that were able to fall into solution. This is normal if you used a lot of pills for your extraction and if you left it sit long enough for the particles to fall out of solution. There is probably very little APAP/paracetamol in your final solution.