During the installation of Drupal core, PIFR re-constructs the install.php URL where it posts to.
This means that any additional installation parameters that have been added by the installer itself are lost.
This breaks my patch in:
My patch adds a new 'bootstrap' GET query parameter during the course of the installation.
Since PIFR is using the same browser as Simpletest, I actually don't see why it has to override those URLs at all.
In core, we're successfully processing and stepping through batch patches like update.php in the same way.