Nice page. Nice mountain!
Interestingly, Thomas Turiano, in Select Peaks of Greater Yellowstone, puts Black Mountain in the Beartooths, while Pat Caffrey, in Climbers Guide to Montana, puts it in the Absarokas, as does the NGS Montana Topo set. Don't know which is actually correct.
I can assure you that Black Mountain is completely within the Absaroka Range. The Beartooths start on the opposite side of the Boulder River drainage, at least a dozen miles east. I'm not sure, but as it remember, Thomas Turiano classifies every Absaroka peak in Montana as "Western Beartooths" so as to not confuse readers with the Absarokas of Wyoming.