Recommended mirroring alternative?

It sounds like you may benefit from a Failover Cluster if all you're looking for is availability. You can run them on standard edition and if you take an N+1 route, you can have two nodes for HA and have one in a DR site ready to take over. You'll need to work on your storage availability for the DR side, but that's a whole other can of worms.

Another option may be Log Shipping since you're already taking log backups every minute. You can ship the logs off to your HA/DR server.

You can get more information on how to do it and the implicatioons for AWS here:

Implementing Microsoft Windows Server Failover Clustering and SQL Server AlwaysOn Availability Groups in the AWS Cloud