Polarizers and LCDs may not be the best idea; LCD displays work by polarizing light†, so knocking back the glare may not even be possible without blocking the image altogether, depending on the screen's direction of polarization and the direction of the glare source.

A hood (suggested in Greg's answer) will be your best bet -- but you can use a box rather than fabric or spend ten bucks putting together a frame out of PVC pipe or a bit of wood molding. It should only take a few seconds to set up (and should be relatively easy to explain to librarians as well). That eliminates the extra person.

As for keystoning, taking the time to set the camera up parallel to the screen is your best option. That will also solve your depth-of-field problem.

† The backlight is initially polarized in one direction by a full-screen polarizing filter. Black pixels are black because the liquid crystal is aligned to allow polarized light through at 90 degrees to the backlight polarizer. The liquid crystal in non-black pixels (or, rather, non-black pixel segments) are electrically aligned at some angle other than 90 degrees. There are a number of strategies for aligning the polarization of the pixel segments relative to the full-screen polarizer; they are out of scope here.