Technically you wouldn’t want a copper heatsink, as aluminum displaces heat better. I will agree that copper will receive heat better though. Perhaps the larger surface area offsets the increased thermal resistance of the joint, that’s really above my ability to test lol. But it would make sense.
Depending on the manufacturer, you typically get test data at 25c and 85c for tc and tj. Some you’ll see a 50c, which is probably closer to a real world application. Maintaining case temp of 25c may be realistic in a freezer lol, and The 85c is usually a sign of undersized heatsinks for application. Depending on the led, you should be able to measure temps and see about where you fall on charts. If you so choose to know anyway.
As far as adding fans, they definitely help with cooling. But you can’t necessarily say the light will be more efficient. Cooling the heatsink will not result in a linear reduction in led temp. If you calculating lumens per watt, the only fair way to do it would be to include the power draw of the fans. That’s why I try to build without them.
Assuming you’re buying heatsinks anyway, then fans, and components to run fans, it’s probably not much if any cheaper than just buying properly sized heatsinks isn’t it? Now if you had some heatsinsks, fans, and most of other stuff needed lying around, you can absolutely make it work. You just eat the extra power consumed to make something out of what you have.