I still haven't figured out how to change the field labels with Javascript, but I did manage to modify the xml view so that the data was displayed properly.  Here is a short example:

<group>

     <!--

         When using dynamic labels in the same group as fields with non dynamic labels,

         make sure the label and the field are broken up in their own div tag

         This way the data will be displayed on the form properly

      -->

      <field name="another_field" />

      <div>

         <!-- Dynamic labels -->

          <label for="field_1" string="Field 1 Name" attrs="{'invisible': [('another_field','!=','value')]}" />

          <label for="field_1" string="Other Field 1 Name" attrs="{'invisible': [('another_field','=','value')]}" />

      </div>

      <div> <field name="field_1" /> </div>

</group>