Consistency checking on a huge graph takes a lot of time. You can speed up that process if your page-cache setting is larger than your graph size. Otherwise the consistency checker will perform a lot of seek operations on your disc. Having locally attached SSDs does help as well. AWS i3 seems to offer this: Now Available: Amazon EC2 I3 Instances, next-generation Storage Optimized High I/O instances - I've never used it myself.
You can also fine-tune the checks being performed by consistency checker, see the -cc-XXXXX options at https://neo4j.com/docs/operations-manual/current/backup/perform-backup/
Another strategy is to skip consistency checking during daily backup and run the consistency check e.g. only once per week.