Will the vinca major vine grow under my Sugar Maple that has established a thick carpet surface of tiny hair-like roots? I'd rather see this growing there as practically EVERYTHING else gets choked out from the Maple roots!
Vinca or english ivy is your best bet given the conditions you describe. The reason the feeder roots are so shallow is either a very high water table, 2-3 feet, or prolonged light shallow watering. Monthly deep root watering, 2-3 feet, without any surface watering will help the tree roots to grow deeper and not cause the problem you described.