Use your cement mixing drill bit to pulverize the wet paper into a pulpy mess.
You can use a cordless drill for this step, but this volume of water and paper will be a considerable drain on your batter.
Mix well. Runny is fine, as long as the paper pieces have been evenly chopped into tiny pieces.
Next, pull the “holey” bucket out of the other and allow it to drain.
This may take a couple of hours to fully drain.
If you’d like to recycle the water, place a 2×4 across the top of the intact bucket and simply allow the water to drain from one bucket down into the other.
After you pulp has drained, more or less, place the intact bucket inside the “holey” one and sit down on top to compress the pulpy paper mess into a round “paper log.”
Allow this to dry for at least 24 hours before flipping the bucket over and tapping the paper log out of the bucket.