find a replacement bmw v8

Hi, I bought a 2002 l322 4.4 v8 (BMW), from a rouge trader, I now need a new engine. This is apparently due to a thermostat fault. The piston housings all need doing and would be looking at nerly 5k for the work. Not going to happen really. I am trying to find a used or refurbished engiene at a more reasonble price but everywhere I phone say there just impossible to find. Can anybody help?

Thanks