JRiver has a built in ASIO driver. I recommend using that one. JRiver has said that it does not modify the bits during playback - other ASIO drivers do. I've never used the ASIO4all driver, but I seem to recall reading in this forum that ASIO4all modifies the bits during playback (take that for what it's worth.)
When you use an ASIO driver, I believe you avoid the Kmixer. The other way to bypass the Kmixer is to go into control panel, find your audio hardware device, and uncheck the box for mapping through the device.
Send me an email if you have any more questions about optimizing jriver -- I've been using it for a few years.