An alternative approach that should look good if it works (I have not tried it), would be to get GD::Graph::bars3d to emit images in SVG vector format through the use of GD::SVG

You can then convert the SVG file to pdf using inkscape's svg2pdf tool. If necessary you can join separate pdf files into one multi page document using pdftk

Disclaimer: I have not tried to use GD::Graph::bars3d with GD::SVG, so I have no idea if it will work, but it it does then the results should be visually appealing, with a small file size.