When browsing proteins in the PDB (protein data bank) looking for design ideas, I found a natural protein with the same sheet/helix pattern as one of the designs (fold III) in the Koga & Koga ideal design paper. In reading further, I learned that some proteins with that shape are called SMR domains, and there are a number of them in the pdb. They have shorter structures and longer loops than the designed proteins. If you were going to modify one of them to make a foldit design, you would have to find a way to shorten several of the loops to make them into ideal loops.
On the PDB pages, you can click NGL, Jsmol, or PV right below the picture to get a movable 3D image of the protein in you browser. In NGL, be aware that the protein colors run from red to blue (instead of blue to red like foldit does). To see the sequence for a protein with secondary structure, click the Sequence tab at the top of the PDB entry, or click Display Files, Fasta Sequence to get the sequence in plain text.