Not ALL batting is illegal. Federation rules DO allow K to bat a grounded scrimmage kick (but not a free kick) toward their own goal line (away from R's goal line, thus preventing a touchback), but it an exception to the batting rule (batting of a pass or fumble in flight or a low scrimmage kick in or behind the neutral zone are also legal acts).
Force is not a factor on kicks entering R's endzone, and a kick remains a kick until possession is secured or the ball becomes dead by rule. So even in #2 with the ball nearly at rest, the motion imparted by the illegal bat by R does not constitute a new force for the purpose of determining a safety or touchback. It will be a touchback, period. K will have to rekick and give R another shot at a return. Is that fair? Perhaps not, but since it was a free-kick, R's choice to give away 15 yards on a rekick may have been preferable to giving the ball up to K (who may gain possession of a free-kick) on his own three. And another kick means another chance to muff, and another chance for K to recover.
It's fun, but I'm sure most will agree that the kicking game provides many interesting challenges.
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