Could you get away with allowing folks to manually paste in the HTML of their own linkedin page, or perhaps upload a PDF version of their linked in page?
Are you scraping the page for input params? Would it be possible to just expose an API (or web forms that point there) to let folks put in those parameters manually?
oy, that would actually have been a much better way of doing it. I was trying to be clever and keep the UI simple, and totally didn't expect to hit rate limits so quickly.