Capistrano deploys break W3 Total Cache minify URL rewriting

I am running WordPress 3.2.1 on Linux on EC2 with Amazon CloudFront. Most of the caching/CDN services are working fine.

However, minify URL rewriting is not working. I get this error in the web admin:

It appears Minify URL rewriting is not working. If using apache, verify that the server configuration allows .htaccess or if using nginx verify all configuration files are included in the configuration.

This is what we see in our Apache error log:

[Wed Dec 14 19:11:10 2011] [error] script
'/var/www/sites/wboard/current/wordpress/wp-content/w3tc/min/index.php'
not found or unable to stat

We have AllowOverride enabled. What's going on?

Edit: This could be related to our Capistrano deploys: http://wordpress.org/support/topic/plugin-w3-total-cache-plugin-loses-minify-settings-on-deployment

What files do we need to clobber to make this work? Is there a good capistrano recipe/workaround?