Based on the NO DIPPING rule, the distance between Deadwood and The Crows Nest Travel Bug Lodge is 1202.87 miles by my calculations. This results in an overall mileage loss of 455.34 miles from the geocaching.com mileage calculation, and 6 skipped caches.
However, the move is still worthwhile, accounting for 8 border crossings (AZ-NM-CO-NE-SD-NE-SD-IA-MN).
Since I am familiar with the scorekeeping of this race, I thought I would post my results here to assist the scorekeeper of this bug.