I am performing a CHOOSE | WHERE | OTHERWISE ... the test for this choose is
to see whether or not my @AvailableInventory is '' (empty).  It doesn't seem
to work, but indeed there is no real value in this attribute.

Well, you have
>   <xsl:when test="@availableInventory=''">
and
>        <xsl:value-of select="format-number(@AvailableInventory,'###,###')"/>
First check which of the two spellings are correct.

I'm thinking
it is padded with spaces.  So how would I perform my test, but trim all the
spaces... or is there another test for "Empty"?

Use normalize-space():
  <xsl:when test="normalize-sspace(@availableInventory)=''">