Options to migrate large database from Sybase ASE to SQL Server with minimum downtime

The problem: Our server database contains 1TB of data. It runs on a Sybase ASE 15.7 server and shall be migrated to SQL Server 2014. The servers will be located in the same data center during migration; an acceptable downtime is 6 hours. We have considered using Sybase Replication Server, as we understand it, this product supports heterogeneous database replication from ASE to SQL. However; we do not have experience with this. Snapshot and transactional replication might be a possible solution. We have some experience with SQL Server Migration Assistant and have successfully migrated the database objects and data in a test environment. However based on 8% test data, we have estimated that a complete migration of production database will take about 7 days. We can only have 6 hours downtime, and are not sure if this product can be used for data migration in our case. For database objects, this product has worked fine. Do you have some recommendations to solve this problem?