I don't know what all you've tried, but I'll toss out what I'd probably do.
The DVI-to-HDMI cable will only work when you have a DVI/HDMI input selected. DVI1 is linked to the DVD input and DVI2 is linked to the Video2 input. I would suggest using the Samsung with DVI1 and a coaxial or optical cable, The Scientific Atlanta with DVI2 and coaxial or optical, and the Sony with Video3 component and optical. With the Sony, though, you have one other consideration: does the component output work under all circumstances, or is it limited to DVD playback? Some combo units like that don't output a component signal from the tuner or VCR, in which case I'd swap the component cable for an s-video cable. You would then need to run DVI-to-HDMI and component to the Kuro and select the appropriate input on the TV (the HDMI input when watching the Samsung and cable box, and the component input when watching the Sony or when you want to view the 1070's onscreen menu). The 1070 can transcode composite and s-video to component, so whichever way you need to connect the Sony the component connection to the Kuro should suffice.