"Disabled" regions re-enable after navigating away and back from module page
I believe I resolved my issue. Both the page callback function and mymodule_page_alter function were in a mymodule.pages.inc file that is linked to in the mymodule_menu function. Drupal doesn't like the hook being in the .inc file, so I moved it to the .module file, cleared cache, and reloaded the page. The form's page seems to be loading the content I want to see and nothing else, even after navigating away from the page and coming back to it later. 

Lesson learned -- I'll just keep all API hooks in the module file unless taught to do otherwise. Or, unless hooks being outside of the .module file isn't possible anyway.