First, ensure that the PostgreSQL user used by Moodle has no connections limit. As you have plenity of RAM, try increasing progressively the max_connections value (300, 350...), work_mem to 2 MB and shared_buffers to 1024 MB (and adjust the effective_cache_size accordingly). If that doesn't do the trick, try something like Pgpool or PgBouncer. Don't forget to restart PostgreSQL to apply the configuration changes
As a sidenote, after you manage to solve the database configurations problems, consider trying Cherokee instead of Apache.