Still, most of your analysis is dead on. If I'm going one rail here, I'm never going soft. My intent would be to send the 7ball to the top rail if at all possible. It requires neither a soft nor hard hit, just a medium speed hit. Going three is reasonable, increasing the risk/reward nature of the shot.
Hence, I think it's a very close choice between a medium speed one railer and the three railer with intention to pocket the ball. We don't know whether this type of three-rail kick is something Josh practices, so we can't be certain of what the right play here was for him.
Josh' choice was reasonable, but there are arguments for the one-railer. I do not believe that the score was a factor in Josh' choice. As Nick Varner once said: "every rack is a race to one." Josh surely felt that the three-railer was his best path to winning that rack.