Thanks for the info. There are many sound cards that just don't have ASIO drivers available. It was worth a shot.
JRiver provides various audio output options. The nice thing is that you don't need a plug-in for these modes, they are built into the software program. However, it largely depends on the hardware capabilities (of the sound card) and the drivers themselves.
Honestly, I'd stick with the regular WASAPI (Push) at this point since it seems to be compatible. As I mentioned in an earlier post, Event and Push will sound the same so there's no need to worry about that particular issue. The difference lies in how the data is sent/received/managed and is dependent on the capabilities of the hardware.