Push Messaging with Amazon SNS, SQS and PHP

Push Messaging with Amazon SNS, SQS and PHP

I want to use Amazon SNS to send time-critical mobile PUSH notifications
to 20 million devices. Each topic can have up to 10,000 devices, and I can
create up to 3,000 topics. Using the Amazon PHP SDK would mean sending
2000 API calls at 1 second each - 33 minutes in total. This is no good for
time-critical messages.
I have created an SQS queue and subscribed that to the SNS topic. When I
send my PUSH message to the SQS queue, it doesn't get delivered - it
remains in the queue.
How can I use these services to send the messages more quickly?
Thank you!