Hi I set-up a Linn DS (not a Klimax) for a friend of mine end of last year.
I tried the DS as a DLNA and as a straightforward DAC (using the "DLNA possibilities" fo the DS for streaming and internet radio only). Both my friend and I preferred the sound using JRiver as a renderer -- don't get me wrong the Linn DS has an excellent DAC, but as a renderer especially if not used for multiple playback areas, its just doing double duty with JRiver. As your set-up has two separate DLNA renderers, I'd recommend simplifying. It should be quite simple to set up (even set-up a different zone and switch to see if you agree with us).
Also, there is the JRemote app for your ipad ... I think it is much better than Kinsky and it can be very customizable to use your custom views from JRiver direct.
Even if you want to continue to use the DS as a renderer (player) rather than just a DAC, you could still use JRemote as a control point, making the limitations of Kinsky and your drop outs sort of moot.