There was an idea to split the mold into 2 halves & enclose the 2 halves in a removable carrier. Pack it with dough when its right side up. Turn it upside down. Remove the carrier, then 1 half at a time to reveal the cookie without disturbing the dough. Unfortunately, there's still the problem of cleaning it.
Some material got stuck in the under extruded areas. That might be solved with ironing. That just leaves the laminations. There might be a benefit to soaking it in water. There is the new $37 polymaker polysmooth PLA which dissolves in alcohol. The $300 polysher sprays alchohol on it for 45 minutes.
The machine doesn't work on recessed areas. Smoothing it with a Q tip might work on recessed areas. There are guys who just leave the part in isopropyl vapor for 12 hours, then wait another 2 days for the part to dry.
The short term may just involve a disposable mold. The lion kingdom hasn't attempted to cook any more cookies in years, so a disposable mold seems viable.
Another idea is wearing gloves to mix the dough. That should eliminate the paw soap & the cleaning.