Finding Nth ranking value based on multiple criteria

Even that don't agree with all your manually putted results, take a look to this, pls..

Thanks Fotis I appreciate the comeback, however the restriction for schools in B2:B21 is not handled and it doesn't look like there is anyway of allowing place #3-#6 to be from any heat number. I also am having a hard time visualizing what $G$2:$G$21 is referring to as it has no way of helping to determine the outcomes.