I found a solution that is adequate for the time being. That is to explicitly set environment variables for the required headers when they exist. Below is an example of the vhost file I’m using.
ProxyPassMatch ^/(.*\.php(/.*)?)$ fcgi://127.0.0.1:9000/var/www/local.mysite/htdocs/$1
SetEnvIf Authorization "(.*)" HTTP_AUTHORIZATION=$1
SetEnvIf Content-Type "(.*)" HTTP_CONTENT_TYPE=$1
SetEnvIf Accept "(.*)" HTTP_ACCEPT=$1
Though I would be interested in a more elegant solution. Preferably one which accounts for all headers and passes them as variables which are uppercased and prefixed with HTTP_ – If that is possible.