Since the power transformer is 110-240/12v DC out, with the appropriate adapter could the frame run on a 12v auto hookup?

If so, is the center or outside of plug-in positive (+).

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Yes, it will

As long as it is 12V DC. Most car batteries support up to 2-3 amps with is higher than the 1.25 max. amps required.

The center is + and out side is -.

However, we will NOT be responsible to any potential damage that the operation could cause to the frame. Since it is an expensive frame, please be careful. ;)