How can I minimize SQL Server data loss in AWS in the event of failure?
Additional to your Full backups you can take transaction log backups every 15 minutes. A transaction log backup contains a list of the changes that happened. During the restore those changes get re-applied.

In the case of a disaster you would restore the newest full backup and then all of the log backups that were taken since that full backup in chronological order. With that you would have a maximum of 15 minutes of data loss. The additional storage is dependent on the amount of changes in your system. Usually it is significantly smaller than another full backup.

You could also add differential backups into the mix: Full backup every 6 hours, differential every 2 hours, log backup every 15 minutes. Most likely that wont safe storage, but it could make the restore a lot faster, depending on your situation of course.

No matter which solution you end up taking, make sure you practice the restore regularly, as it is not completely trivial and a disaster is not the right time to try to figure out how it works.