How to handle Pinpoint SMS message per second rate (MPS) for broadcasting to large group of phone numbers?

Hi - Apologize for a long question. I am looking into using SNS topic or Pinpoint SMS channel to send notification messages to a group of recipients using SMS (subscribers that agreed to receive sms messages).

The requirement is to send a single message that will be broadcast to the group (some groups have a few hundreds SMS endpoints). I already registered a company under the new 10DLC requirement and waiting for my campaign registration approval (mixed use case). I understand that with my mixed use case campaign, there will be a quota on how many message parts I can send (75 per minute for ATT & 2000 per day for Tmobile).

My question is what will happen if I send a SMS message that will broadcast to large group of recipients using SNS topic / Pinpoint project that will exceed the message part per minute rate imposed by the carrier based on my campaign's rate limit (e.g. more than 75 ATT phone numbers)? Will Pinpoint / SNS throttle and reject my send request? Or will Pinpoint / SNS accept my request but sending the SMS messages over a period of time? The message does not need to reach everyone at the same time but preferably within reasonable time frame like a few minutes.

I have been searching for quite some time but I could not find an answer. Any advise on how I should setup/design the system using long code? Short code is out of the question due to high monthly cost as this is for a non-profit community characterized by infrequent messaging but large fan-out base.

Thanks for your help!