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Couldn't you turn the slinky on its side and scale it your max print size? Make sure each link is 1.75 mm. Then switch the filament halfway through. Use the finished print for filament.
BUT...
This will be a very hard print, with or without supports. It will also be hard to get all the layers to line up. But that would theoretically work, although each color change would be very close.
Just a thought!