Steven ZahmRE: Scenario 1, is it possible to extend the scope of the keyword search so that it searches outside of the category specified in the shortcode? This would be ideal and simplify everything, requiring only one shortcode instance.
You can try the code from this tutorial.
RE: Scenario 2, is it possible to have search results displayed on a different page – a different template as it were – which contains a single shortcode with different listing parameters?
Yes, that is what the home_id option can help with this. Can you describe how it did not work? I see you are using an older version of Tile Plus. Perhaps that is why it is not working.
As a third option, you could try the Custom Entry Order extension. Since it sounds like you only need to display the senior management first. I believe that would accomplish your goal.
Similarly, I would suggest the Custom Category Order extension. That way you can order the categories in the drop down in the order you wish without have to use number prefixes.