See you ****ed up. It was a solid effort, but you showed you don't really have a strong grasp about how advanced analytics and probabilities work in sports. It's pretty weird actually how frequently you toss out buzzwords and cliches that you either don't get or don't apply, regardless of sport. "Searles has a propensity for only starting upperclassmen so Linder and Odogwu will start," despite evidence and logic pointing against that.
Data compiled over half a decade of MLB seasons this decade show that the reduction in run expectancy when going from 1st and 2nd no out to 2nd and 3rd with 1 out is negligible (less than .06 runs lost per inning). Not this 10.4% you quoted. So statistically there is almost nothing lost from bunting in this situation. The run expectancy for runners on 1st and 2nd and no outs is 1.44 runs and for runners on 2nd and 3rd and one out, the run expectancy is 1.38 runs. Keep in mind this is in ANY instance that there is almost no difference in the two actions, let alone in a tie game in the last inning. But you need to take it further (and this is where you got lost). With runners on first and second, no outs, the probability you score 0 runs is 37%, 1 run is 23%, 2 runs is 16%, 3 runs is 12%, and 4+ runs is 12%. With runners on second and third, one out, the probability you score 0 runs drops to 33%, 1 run increases to is 27%, 2 runs increases to 22%, while 3 and 4 runs decline to is 9% and 8%.
So what does this tell us? Taking those numbers into account, by bunting you actually increase your chances over scoring a run from 23 to 27% and decrease your odds of scoring 0 runs from 37% to 33%. You're increasing your odds of scoring a run at the expense of scoring 3 or more runs. Given the fact that we needed 1 run to walk off and win the game, coupled with the reality of the situation (keep in mind these statistics represent all players and all situations so their has to be a situational element applied to your data), that you have a below average hitter at the plate and your 3 and 4 hitters coming up to bat, and as mentioned a chance to walk off and win the game (if this was say the 3rd inning of a game it can be argued you're slightly limiting your chances of a big inning by sacrificing an out) it is obviously the right decision to bunt over those runners and let your best hitters come up with a chance to win the game.
Good try on the analytics though.