I hope that dBasement understood that I would not dig out good bearing soil just to put it on engineered fill. Of course, if the soil is poor, one could remove and replace. 2x might not be large enough for strip footings that normally have pressure bulbs to depths of 3.5 to 4x footing width. One might consider the use of digging out partially and using geogrids (see paper by Braja Das and Adel Hanna on Model tests for shallow strip foundation on granular soil in ASCE Special Publication No. 16, Special Topics in Foundations (1988).