My experiment was a success! After discussing the possibilities with an employee at Hobby Lobby, I came to this solution.
Using a glass jar, some recycled paper and a bit of blue dryer lint, I tore the paper into fairly small pieces and added the lint and hot water. While it soaked, I did steps 1-3 below. The dark blob on the left side of the jar is the lint.
Step 1: Cut a sheet of perforated plastic canvas into rectangles 2.5"x3.5", and attaching two pieces of wire to the short sides of one, leaving the second rectangle alone.
Step 2: Using the LID half of a plastic box designed for trading cards, this made my "deckle" and the plastic canvas pieces became the screens.
Step 3: Removing the screen from the box, I added a small amount of water and white glue, then replaced the handled screen. Please note: the picture shows the water in the bottom of the box, not the lid. This was an error; with the handles, the screen doesn't fit flat like it does in the lid.
I used an immersion blender (stick blender) to blend the paper and lint. I ran into a bit of a snag, because the dryer lint also had dog hair and Wendy hair, which clogged the blades of the blender. Once I cleaned it out, it worked fine.
Step 4: Using a measuring scoop, I dropped around a 1/3 cup of my paper pulp into the box on top of the handled screen. I added the pulp gradually, because I didn't know how much it would need, so the scoop in the picture isn't full.
Step 5: The box on the left shows the top screen pressed in place. The box on the right shows the pulp swimming on top of the handled screen.
Step 6: Carefully lifting out the screens, I squeezed out the extra water over the box, and set the screen to the side while I did that with the other box.
Step 7: I put the two screens with their pulpy filling onto a washcloth folded in half, then folded then pressed the free end of the cloth firmly onto the screens.
Step 8: After blotting the worst of the water out of the screen sandwich, I peeled the top screen off s-l-o-w-l-y, starting with one corner. Then I pressed the handled screen pulp-side-down onto a dry paper towel on newspaper to blot again.
Step 9: I then carefully peeled the handled screen off of the much-dryer pulp (below) and set it on glossy newspaper ads to dry a bit.
Step 10: On the left, you see what I ended up with after Step 9. The one on the right is what the paper looks like mostly dry, after I had a go with the hairdryer.
I'm so excited that this worked! Of course, I got way carried away with the blue paper, and now have much pulp to process. Eh! Live and learn!