I have tried a number of screencapping services but none so far can cap a PDF and make a thumbnail.
I have also seen scripting for this purpose but it all relies on installing Ghostscript and ImageMagick and this app will be on a shared server and it does not have them installed.
Admins of the site will be uploading new PDFs constantly and want to have thumbnails of page one displayed. Anyone seen a webservice that can produce these?
You should probably really change your (shared) hosting to one where at least ImageMagick’s convert is available:
Working around such limits is hard and paying a few bucks more (or even the same amount somewhere else) is most certainly worth the effort of switching.