What is the best SQL server backup strategy for large DB with few tables and lots of immutable data?
I think you should look into log shipping once you get it setup your 10 minutes logs can be shipped to the server, so only changes are updated. 

Assuming the log shipping destination is also where you want your backups kept, you can do backups there.  Other then the initial backup, you can run for years and only ship the logs. 

You could take full backups at both your primary and log shipping destination. That way you would have backups in both locations, and your only data moving daily is the logs being shipped. 

Alternately you can use AlwaysOn instead of log shipping for the same effect. 

Licensing: I am not an expert on licensing, but my understanding is that if the Log shipping (or AlwaysOn) destination instance is for DR only, there is no additional cost.