Offsetting reporting Load from one server to another
One issue with your trigger implementation is that if the reporting DB or DB Server goes down for any reason or stops accepting requests, your prod systems will stop as well.  Also if you make schema changes note that you'll need to do that on the reporting table as well.  Your solution will work, it just isn't ideal.  SSIS won't help with the schema changes but at least if the reporting server can't accept requests prod will still keep working.

Replication is nice too if you have a primary key on the table and meet all the replication requirements.  Just note that replication (IMO at least) requires more experience to fully understand than a pure AlwaysOn or SSIS solution.  Replication requires agents and extra security.

SSIS could work at the frequency you're using it for, maybe it just isn't ideal.  If you're OK with losing in flight transactions when the server reboots you can look at Service Broker which will be much more near real time but Service Broker has a even higher learning curve than AlwaysOn.

Personally I would stick with Replication or your current SSIS solution.  Both require some tuning and testing but both have their advantages as well.  SSIS at least won't deal with all the security and agents that replication requires.

Are you open to using 2014 standard edition read only replica in an AG?  It gives you a lot more options, let's you query the entire database, gives you a nice near real time complete copy, and isn't too difficult to setup but absolutely much more difficult to setup than a trigger.  Edit: Sorry I just saw that you tagged SQL 2008 R2.