3.0.1 won't properly install to subfolder

I am attempting to setup a WordPress 3.0.1 site on my server manually, so that my WordPress index.php is stored in the root folder, but my WordPress installation is in its own subfolder. I have done this dozens of times with prior versions of WordPress, and several on the very same server with the very same configuration under which I am experiencing this error.

1. I downloaded the .zip file direct from www.ads-software.com via wget, then unzipped it, and subsequently renamed wordpress/ to cms/.
2. I then moved the index.php file from cms/ to the root directory and edited index.php to read:

   require('./cms/wp-blog-header.php');

3. Then I duplicated wp-config-sample.php to wp-config.php, edited it to reflect my verified DB login info, and added:

   define('WP_HOME', 'https://mydomain.com/cms');
   define('WP_SITEURL', 'https://mydomain.com');

4. Upon visiting mydomain.com (which obviously isn’t the actual domain), I’m redirected to https://mydomain.com/wp-admin/install.php which results in a 404 error.
5. If I manually visit https://mydomain.com/cms/wp-admin/install.php, I see the install page, however, it is not styled by CSS.
6. When I view the source, I see that the CSS is referenced at

   <link rel='stylesheet' id='install-css'  href='https://mydomain.com/wp-admin/css/install.css?ver=20100605' type='text/css' media='all' />

   This seems to indicate that the WP_HOME parameter in my wp-config.php file is being ignored by the installer.

7. I have tried this under two different domains on the same server and experienced the same exact problem. I did not, however, experience this problem with WordPress 3.0 using the same exact installation method just two weeks ago.
8. If I install WordPress into the root folder (without the cms/ subdirectory) everything works fine. However, this obviously makes my install more vulnerable to hack attempts and is thus undesirable.

Has something changed that WordPress no longer supports subdirectory installs, is this a bug in WordPress 3.0.1, or am I missing something?