Strategy for cloud tier backup schedule

We tier monthly and yearly backups from avamar/data domain to aws.  That means that at the beginning of a new month we can get hit with a large amount of data being pushed to the cloud as all the monthlies are set to be the 1st day of the month.  Is there any way to stagger this?  Other ideas?  The best I'm coming up with would be to have the data domain only run data movement on Friday nights so we don't kill our internet line during normal business hours. 

I find it interesting that the help says that data movement occurs no more frequently than weekly, yet ours shows daily.

Data Domain OS 6.0.2.20-587212