The response from Tridion Support confirmed that this is not supported for database publishing:
documentation for the root element and path attribute says they're
used for the filesystem storage provider. So unfortunately it looks
like this isn't possible without additional customization work.
Mark, not sure if you considered using custom Template Building Blocks. Although not a quick solution, in the custom TBB, we should be able to update the root path just for PDFs by calling the Engine.AddBinary() method and specifying the path (Structure Group) where you'd like the PDFs to be published.
So, something like this in the TBB should deploy only ...