I don't think the forging (damascus) method will work because you will need to get the copper temperature close to or above the melting point of the aluminum just to make the copper workable. For the layers to weld together you would need to be at an even higher temperature.
the copper and alloy forge in a range from 1100 to 1650F. Aluminum (pure) melts around 1220F. Pure copper melts around 1983F so I'm not sure how well the turn-and-pour method would work.The closer you can keep the copper to it's melting point the less the materials will alloy but the less working time you will have. The skin will begin to form the instant the melted metal touches the mold. The 750 degrees of superheat into the aluminum might cause the two metals to react.
It would be relatively easy to try an small scale experiment with a little copper, aluminum, and a torch to see if they are in anyway compatible. You might need 2 torches and 2 crucibles to get everything hot at the same time... Melt the metals and pour into a mold (a small piece of steel pipe maybe?) Instead of spinning, you could probably just use a steel rod to stir the mixture together. It would also benefit from pre-heating the mold and argon or nitrogen blanketing the entire process. Sounds like a fun experiment but I don't have any metalworking tools/torches.
Just a warning -- molten metals are DANGEROUS! Make sure everything the melted materials will touch is dry. A small puddle of water in the mold will make superheated steam that will send the still liquid metal straight to the ceiling.
BTW I used to work as a Process Metallurgist in a steel melt shop but we were always trying to make homogenous alloys not pretty things.
Another idea if you are really good on the lathe -- turn 2 spirals that would thread together (think interlocked coil springs) If the fit was tight enough you could turn to whatever final shape you desired or fill with epoxy and then turn.
Good luck and hope all turns out well!