Replace default Drupal Garland theme during installation

I'm writing an installation profile and want to switch default system theme (Garland) to my own theme. The theme should replace Garland on the first step - when I choose installation profile. On this stage Drupal is not bootstrapped, so I can not set appropriate DB variables.

Any ideas how to do that?

Short answer, you can't. It's fairly hard-coded in _drupal_maintenance_theme():

// Install and update pages are treated differently to prevent theming overrides.
if (defined('MAINTENANCE_MODE') && (MAINTENANCE_MODE == 'install' || MAINTENANCE_MODE == 'update')) {
  $theme = 'minnelli';
}