How can I use the keyword box to add keywords to a sequence of pictures without using the mouse?
The solution is actually quite simple.
Aperture => Commands => Customize

This brings up means to map any key to any command.

The desired command is "Add New Keyword"  It defaults to being mapped to command backtick, which I find awkward.  I remapped to Command K.  This overwrites a command used for stacks, but I don't use stacks much.

This allows me to go Command right arrow to select the next photo, then command-K to put the cursor in the bottom add keywords window.