While it is not elegant, I did come up with a way to do it using CellTags (CellStyle would work too, I think). The only problem is that this approach requires deleting input cells and formatting the new notebooks to retain the formatting of the original notebook. I would still really like a solution that can create the PDFs from within the original notebook.
noteCells = Drop[Split[Cells[], CurrentValue[#2, CellTags] =!= "NewNote" &], -1];
pdf[c0_, n0_] :=
Module[{c = c0, n = n0, nb},
nb = CreateDocument[];
NotebookWrite[nb, NotebookRead[c]];
NotebookDelete[Cells[nb, CellStyle -> {"Input"}]];
Export[FileNameJoin[{NotebookDirectory[], "test-notes-" <> ToString[n] <> ".pdf"}], nb];
NotebookClose[nb];
]
MapIndexed[pdf[#1, First[#2]] &, noteCells];