Use print_pdf in the background on node save? As the Print module's creation of a PDF can be quite slow (and use a lot of memory/CPU), is it possible to save a PDF into the public:// files area each time a node is saved?

Has anyone done this? Presumably you could call a save-PDF function on hook_node_presave but I'm not sure what the next step is. Call a print-PDF function with a file path? Where is that print-PDF function and how would you call it?
The function used from that module to output PDF is print_pdf_generate_html(), which gets a filename as last parameter.

To understand what to pass as first argument, see print_pdf_generate_path(), which is the function calling print_pdf_generate_html(). In particular, see the following code.

$print = print_controller($path, $cid, PRINT_PDF_FORMAT);
if ($print === FALSE) {
  return;
}