Is your firewire cable plugged in for camera control? Is so, you may try removing it. We’re not FCP or JVC 250 experts (just got both and have zero experience) but had a similar problem. Turns out we were capturing thru the Firewire port.
We got the AJA Kona 3 and BAM! It looks AMAZING! But we had to do the following to make it work:
1. Put the Kona in the 3rd slot on the G5. Would not work anywhere else.
2. Deinstall / reinstall the Kona drivers
3. Test the camera to the Kona Utility (with FCP closed)
4. Set the frame rate / format in the Kona Utility
5. THEN and only then open FCP. Set formats to match the Kona.
Worked when we followed these steps, failed when we didn’t. Could not possibly be happier with the video quality or sharpness of the camera. Everyone who sees it is amazed.