From your description, it seems that Postfix is the one that is blocking your incoming e-mail; the line specifying the 'check_policy_service' does indeed cause this behavior. If you tell Postfix to check if a policy server will allow the message, and that server doesn't respond, Postfix will not allow the message through.
It seems that you need to have a harder look at the way the postgrey stuff is set up, because it does not appear that a live postgrey process is listening where Postfix expects it to be listening. I commend you to the manpage for netstat, a utility that will list for you the active sockets of a particular type, along with the program that is responsible for the connection (if you ask nicely).
Your post indicates that your setup is using a loopback TCP connection as the conduit between Postfix and postgrey (inet:127.0.0.1:60000). This indicates that Postfix will send a query on that TCP port, and expect a reply there. But your log report indicates that postgrey is trying to bind to a (unix) socket, not a TCP socket, so it is unlikely that these two processes will be able to exchange messages successfully.
I am not sure what caused this change, but it needs to be corrected: either you need to convince postgrey to listen on 127.0.0.1:60000, or you need to tell Postfix to talk on the unix socket /var/run/greylistd/socket. I will leave as an exercise for you to work out which you like better, and how to alter the relevant configuration file to make this so.