I understand all you are saying except for the part in red.. Why are you taking the risk of playing for win in the 10th, 11th 12th when you are the home team in the 9th, tie game?
A bird in the hand is better than two in the bush... You have a runner on... in the 9th... No guaranty you will any other inning. So increase your chances to score anyway you can and finish it.. Also. we had basically one pitcher left.... That has to be factored..