Broad question, but at first sight my answer would be that - if you let them go as far as the PDF - you're making things very difficult already. If they are still using Quark XPress, there are far better ways to do this kind of thing and similar approaches are actually be used by quite a few publishers out there.
1) Look into generating both PDF and XML out of Quark XPress. It's fine that they don't want to change their ways but they have to create PDF out of Quark anyway; also generating XML is not a really big additional step. In fact (warning - affiliation!) there are tools who can make all of this into one step. You could write AppleScript for example to steer the process, but something like axaio MadeToPrint will automatically generate both the (correct) PDF and an XML file after people clicking "export".
2) Once you have the PDF and the XML of the same content, use the PDF for print (just as know) and then write some code to convert the XML into whatever you need on the web site. If the coding is done on the web site itself, you might not even need to tweak the XML coming out of Quark; simply make the site smart enough to pick up whatever bits and pieces are necessary.
Broad answer on a broad question; hope that was what you are looking for...