If I were working in that environment, I'd concatenate the multiple PDFs into one so I could search the entire set from any PDF reader. It's probably not as convenient as a web interface with a more sophisticated search facility, but it solves part of the problem fairly quickly.
To concatenate multiple PDFs:
gs -q -sPAPERSIZE=letter -dNOPAUSE -dBATCH - \
sDEVICE=pdfwrite -sOutputFile=ALL.pdf *.pdf
Adjust the paper size and the order of the input files to taste.("gs" is the Ghostscript command.)