First, I must say your version looks definitely better than those I’ve had with e.g. wkhtmltopdf or any of those html2pdf softwares, so kudos to you !
I am also working towards generating a PDF automatically each time the doc is updated (hence the 1-page html version of the manual that you probably used to create this document, and the CSS simplification of the last few months). Though, I’ve come to realize that what remained to be fixed couldn’t, as HTML is definitely not a “physical document” format. There are a few CSS tricks, like paged medias, that would probably help but we are a long way from getting a serious looking PDF from what we have. Handling tables, floated screencaps and customized styles, as well as having a proper PDF hierarchy, are all going to be a lot of work, if even feasible. We could migrate the whole documentation from the custom Python scrips we are using now to e.g. Sphinx (that produces nice PDFs and has an integrated search) but that needs converting the whole documentation to reStructuredText, and would need approval from all the team.
What would be left for you to do is a lot of work on all the HTML/LaTeX to have a nice PDF, and this document (and all your work) would be obsoleted by the first doc update, unless you find a way to automate the nice-PDF generation.
Regards, and again, congrats for the doc even as-is, don’t let me discourage you !