Use current_time() and time constants for readability and reliability.

time() should return the same timezone consistently, but current_time() guarantees UTC
Initialize sitemap ping actions within the setup method for consistency
Lower timeout on ping request and reorganize request parameters for cleanliness.

Since wp_remote_head is non-blocking, we set the timeout very low so that it's killed immediately after it's sent. This speeds things up considerably.
Add protocol to Google ping URI