SQL Server mirroring / failover alternative
I'm not sure I understand, you state you are going to use mirroring, in standard it is still available so why can't you use that?  Or is the question that is there anything else available?

You can also use Failover clustering in standard edition, the limit is you can only use 2 nodes but I don't see that as an issue for your request.

Also, if you are using any virtualization technology (VMware, Hyper-V etc) there may be options that you can speak to your virtualization about which are edition (not to mention software) agnostic.

Mat