It seems that the best option may be to tell Word to print, but click the "Print to File" option. (It will then ask you for a file name.) Assuming that you were printing to a Postscript printer (and you most probably will be), this will fool Windows into generating a postscript file.
Some of these postscript files are huge, so you can try running ps2pdf on them on any *nix machine; this often gets a great improvement in space, hence in the time to load the file. This will help your friendly TA a lot.
If your machine does not have a postscript printer as the default, you can install one. Details can be found on pages here or here, or here (local instructions). Then you can select this installed postscript printer to print to (except that you will also check "Print to File"), and the output will be in postscript.
We tried the Neevia Document Converter recently to convert Word to PDF; it is non-intrusive and not too slow (80 page text-only Word file to PDF in 30 seconds). If you are having trouble with the above method to generate PS, this may work for you. Another option is gobcl.com.
If all else fails, you can use the TOM conversion service, though we would rather you didn't. It makes huge files of inferior quality.
On the *nix machines: use ps2pdf. On windows machines, use a program called Adobe Distiller. Also, the web site ps2pdf.com accepts PS files and returns PDF files.
On *nix, the program is pdf2ps. On Windows machines, follow instructions for converting Word to PS.
I have seen a tool called mpage, but the andrew machines do not have it. The util here is psnup, used like this: psnup -nRxC -p outputfile filename, for example: psnup -n3x2 -p rec1_6up.ps recitation01.ps.