Lets stay with your analogy. You blew up a cubic foot of dirt, in New York city, how much landed in Japan ? Now multiply distance that distance by 5,000 and you have the minimum direct flight. It would take your fungus 5,000 roundtrips from Japan to NY and thats if it went straight.
Now think of the earth as a globe and the infinite directions that something leaving earth can take.
With all that the chances that Mars is in the right place when your spores from the dirt pass by is equally infinitesimal.
Little bits of yummieness. :-)