By "throttling", blue_cowdawg did not mean blocking, but rather limiting the rate at which new messages can be sent

You might consider adding a sleep(1) in your loop.

Also, maybe you should consider using a list service. You send your message to the service, then it forwards it to the list subscribers.

Since you are already using Google, Google Groups is one list service to consider. In my (limited) experience of subscribing to Google Groups, subscribers don't have to have a Google account to do so (assuming it hasn't changed since the last time I used a non-Google account with a Google Group).