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 tried that, and it gets me part way there, but the internals of the WordPress index.php come into play to prevent this being a solution.
1. WordPress wants the "Page" name to come last, so I followed your suggestion, but with "app" moved to the end.
Same idea as your rule, but rearranged. See .htaccess appended below.
2. The REQUEST_URI is "alpha/beta/app", and the QUERY_STRING "p1=alpha&p2=beta", ...
but the WordPress index.php comes into play and seems to do a REDIRECT (so my app never gets a chance to run)
so that REQUEST_URI becomes "app" and QUERY_STRING is empty. My app code runs, but now it is too late; the parameters are gone.
Also, I should go ahead and tell you that I know very very little about Wordpress, and how it handles things. Would it be feasible to move this part of your project away from Wordpress?
In WordPress, ... in addition to your (blog) "Posts" you can create a "Page". The typical example would be an "About" page.
In my case, I created a paged called "app". What is nice about this is I can use WordPress as a content management system, I can change Themes easily, etc. ... but embedded inside the page I can put vanilla PHP code.
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.