URL Rewriting and Rack base paths

Question

I'm trying to set up a Rails website on Bluehost and I'm having trouble with the path helpers. As I don't want to monkey-patch Rails, I'm trying to solve this through .htaccess. Here's the scenario:

1. I'm hosting www.engradado.com on public_html/engradado, which points to rails_apps/engradado/public

2. I'm rewriting www.engradado.com to point to www.engradado.com/engradado, through this public_html/.htaccess file:

   # BlueHost.com
   # .htaccess main domain to subdirectory redirect
   # Copy and paste the following code into the .htaccess file
   # in the public_html folder of your hosting account
   # make the changes to the file according to the instructions.
   # Do not change this line.
   RewriteEngine on
   # Change example.com to be your main domain.
   RewriteCond %{HTTP_HOST} ^(www.)?engradado.com$
   # Change 'subdirectory' to be the directory you will use for your main domain.
   RewriteCond %{REQUEST_URI} !^/engradado/
   # Don't change these line.
   RewriteCond %{REQUEST_FILENAME} !-f
   RewriteCond %{REQUEST_FILENAME} !-d
   # Change 'subdirectory' to be the directory you will use for your main domain.
   RewriteRule ^(.*)$ /engradado/$1
   # Change example.com to be your main domain again.
   # Change 'subdirectory' to be the directory you will use for your main domain
   # followed by / then the main file for your site, index.php, index.html, etc.
   RewriteCond %{HTTP_HOST} ^(www.)?engradado.com$
   RewriteRule ^(/)?$ engradado/ [L]
   

3. Here's my rails_apps/engradado/public/.htaccess:

   Options -MultiViews
   PassengerResolveSymlinksInDocumentRoot on
   #Set this to whatever environment you'll be running in
   RailsEnv production
   #RackBaseURI /
   #PassengerAppRoot /home2/engradad/rails_apps/engradado
   RackBaseURI /engradado
   SetEnv GEM_HOME /home2/engradad/ruby/gems
   

4. Whenever I call a path helper, e.g. root_url or news_path, it prepends /engradado to the path, so instead of root_url => "http://www.engradado.com/" it prints root_url => "http://www.engradado.com/engradado/", and news_path(1) => "engradado/news/1" instead of news_path(1) => "news/1".

How can I solve this so /engradado isn't prepended to the url?