Sounds like you want to be able to control the Kickr resistance through the Elemnt, but have the Elemnt record the power numbers from the Quarq? If that's the case, then I think the answer is that you can't do it.

My assumption is that while the Elemnt can connect to multiple devices at once, it can't connect to multiple devices that are transmitting the same data even though it can store multiple devices in it's pair list. I have my Quarq and Powertap wheel stored in my Bolt. Quarq is on my road bike that I use outside and PT is on my bike that sits on the trainer. One day I moved the Quarq over to the bike that sits on the trainer and wanted to use the Quarq power data but still pick up the speed from the hub of the Quarq. Wouldn't let me connect to both.

If your Wahoo is picking up your Quarq PM values, it shouldn't pull your Kickr values to TrainingPeaks/Strava or other. At least mine doesn't.

While I don't think what you're experiencing is correct, one thing you can try is to use the wahoo utility phone app and enable "Control w/ ANT+ Power Meter" then enter in your Quarq PM. This should have it match the values. Edit: This is probably good practice either way