SQL Server Replication or Backup via sftp
In order for replication to work, the publisher and subscriber need to be able to talk to the distributor directly so I don't think this will work in your current setup.

Depending on the amount of data you're producing, a version of log shipping may give you what you're looking for, but you are limited by the database being in a state that allows you to restore further logs and you will still get some disruption when the logs are restored.

The two 'seamless' options I can think of to give you more frequent updates are:
1) restoring your backups to a new database on the on prem server and then using SSIS or stored procedures etc to push this into your actual database(s). 
2) using Enterprise Edition and AlwaysOn groups to restore the data to the primary server, which will then be replicated over to the read only secondary which your reporting services etc are pointing at.