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PSK allows R to retain possession of the ball after the kick and still have the penalty enforced. In overtime, R never gains possession of the ball and keeps it. R gets a new series at a given spot. If you allowed PSK then you would be trying to mark off yardage from say the 10 and make it first and goal from the 20.
Each series in overtime is unrelated to the other. The only penalties that may carry over are from fouls that were dead-ball or unsportsmanlike or succeeding spot enforcement. The foul by R in your situation is a previous spot enforcement.
In your example R's foul must be dealt with prior to the next series starting. So now K gets to repeat 4th down at the 4 yard line.
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