After following your suggestion, I dove into the WordPress index.php and followed the flow for how it routes you to a particular page.
I found that I can insert my own PHP code to scrutinize the REQUEST_URI, QUERY_STRING, etc, so I can pull out the parameters needed for my app, and then edit the REQUEST_URI so WordPress is none the wiser, ... and simply displays the proper page. ... then my app code gets invoked, ... plus it has access to my parameters. Solution found.
I found that I can insert my own PHP code to scrutinize the REQUEST_URI, QUERY_STRING, etc, so I can pull out the parameters needed for my app, and then edit the REQUEST_URI so WordPress is none the wiser, ... and simply displays the proper page. ... then my app code gets invoked, ... plus it has access to my parameters. Solution found.