Throttling S3 commands with aws cli

I'm running a backup script using AWS CLI to perform an S3 sync command every night on my MediaTemple server. This has run without fail for months, but I updated my Plesk installation and now every night, when the backup script runs, MediaTemple disables my server due to excessive usage. The limits I seem to be crossing are as follows:

RESOURCE INFO:
Packets per second limit: 35000
Packets per second detected: 42229.11667000000306870788
Bytes per second limit: 50000000
Bytes per second detected: 61801446.10000000149011611938

They also include a networking snapshot at the time they take the server offline which includes many open connections to Amazon IP addresses (9 at time of the snapshot).

Is there anything I can do to throttle the connections to AWS? Preferably I'm looking for an option within the AWS API (though I haven't seen anything useful in the documentation), but barring that, is there something I can do on my end to manage the connections at the network level?