No, I don’t know of any Ku-band SDRs. However, down-converters do exist. They’re called LNBs (Low-Noise Block down-converters).
The DC3 project will be based on a Maverick MK1-PLL. The LNBs are powered through the same coax that the L-Band signal comes down on. I bought mine from E-Bay. They also sell them on Amazon.
I use a Bias Tee to inject the DC voltage to the LNB. It wants 13 or 18 V depending on the polarity you select. The bias tee blocks DC from going towards the receiver.
I bought my Minicircuits Bias tee from E-Bay. I also made one. I can show you pictures and a schematic if you are interested. I power my bias tee with my lab supply.
The DC-3 project will include the Bias-Tee as part of its circuitry.