Robert Kourik has a book devoted to roots at
http://www.robertkourik.com/books/roots1.html . According to his site, those 18 inches of soil you have host 90% of the roots anyway:
Did you know?
• About 90% of a tree’s roots are to be found in the top 18 inches of the soil.
• At the end of its first year’s growth, an apple tree can incorporate as many as 17,000,000 root hairs with a total length of well over a mile!
• The glorious magnolia (Magnolia grandiflora), can grow roots 3.77 times wider than the dripline.
I also recall that Mark Shepard, in Restoration Agriculture, cited the Hundred Horse Tree, a 4,000 year old chestnut, that grows on bare rock on the eastern flank of Mt. Etna in Italy. It has the largest girth of any tree ever recorded, according to him. The Canadian Shield covers about half of Canada, and there are plenty of large trees growing there. Absence of a taproot doens't guarantee failure at all.