Situation 2.10.1 B talks about an error being found after time has expired in the game, but before overtime begins. It says that the error can be corrected.
Although we're talking about halftime in this case, I would think the error can be corrected. The ball wasn't made live after the first dead ball following the error.
Like you said, I'd shoot the "one and one" with the lane clear, then use the AP arrow to determine who gets the ball to start the second half.
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