Yes, you are correct in saying a 12 ft. wide dozer would not compact the center portion of the core. However, it has been my experience that a dozer does not do a very good job of compacting earth fill anyway. Pounds (psi) of force exerted downward by a 35,000 lb. dozer does not exert nearly the same force as a 7,000 lb. farm tractor! The surface area in square inches of a dozer's tracts is quite large compared to a rubber tired piece of equipment. Dozers are designed to "bouy" themselves and therefore do a poor job of compacting soil. A small 8 ft. wide Earth Scraper, Sheepsfoot Packer, Vibratory Packer or even a small Farm Tractor will do a much better job on a core trench in my opinion.

Ed