.htaccess, multisite, and cookie errors

We have a multisite wordpress installation that uses subdirectories for the various sites. When we tried to map some of the sites to domains. This didn’t work at first, so we put the following for each mapped site into the .htaccess file:

RewriteCond %{HTTP_HOST} ^(www.)?site1.tcc.oursite.com$
RewriteCond %{REQUEST_URI} !^/wordpress/site1/
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ /wordpress/site1/$1
RewriteCond %{HTTP_HOST} ^(www.)?site1.tcc.oursite.com$
RewriteRule ^(/)?$ wordpress/site1/index.php [L]

This allowed all of the mapped sites to work. However, we can’t log into them and we can’t reach their dashboards when logged into unmapped sites. When we try, we get the infamous ERROR: Cookies are blocked or not supported by your browser. You must enable cookies to use WordPress. We are trying to log in as a superuser. Trying to switch to the dashboard for a mapped site brings up the log in screen.

We’ve tried the cookie_domain fix and variations on this that we’ve found on the Internet. So far, nothing has worked. Any help would be greatly appreciated.