You are starting with the right approach, but in order to truly copy an extraction, you need to homogenize your standard with the fecal matter. Next, I think centrifugation would be best to get rid of the solids.
Since your drug is soluble in water (you are able to spike it), it is possible that the recovery in the centrifuged water is high. I would load the supernatant water onto a conditioned solid-phase extraction cartridge and then follow standard protocols to clean up and elute.
This was where my question regarding the nature of the analyte came from. If the analyte has a basic function (an amino group), I would already in the extraction from the feces add acid, best probably phosphoric at about 0.1 N. Then I would use a mixed-mode ion-exchanger, Oasis MCX, for capturing the analyte, followed by washing and selective elution. If your analyte is not a base, but an acid, then an anion exchanger can be used. I cone give you more details on the protocol, if you tell me if the analyte contains an acid function, or a base function, or has none of these features.