I inspected the medal today.
The reverse die (THE HAWAIIAN MINT $) is from 2TC-55/2TC-56 (Hawaiian Sand Dala-Island of Maui) and/or 2M-138/2M-139 (Hawaiian Sand Dala-Big Island). The Kalakaua and Liliokalani obverse dies are from 1983 21mm Kalakaua and 1983 21 mm Liliuokalani medal (too many to list)
The obverse was originally blank. The Queen Liliuokalani counterstamp was first struck. Then the Kalakaua counterstamp was made. The letters and numbers were then struck.
M&R incorrectly states “…dies struck as a pair.” The overlapping of the counterstamps clearly shows that the two dies can only overlap. In addition, the Kalakaua counterstamp is over the Liliuokalani counterstamp.
Also, the listed catalog price seem too low. I can surmise that the coins given away in 1983 were mishandled as a curiosity piece (touched, inspected, and passed around). Not many retained its original mint state condition. It is also, highly unlikely others were made and sold.
From my reference documents, 2MB-199 may be the only medals to use 21 mm counterstamps. It is also the only medal to have two obverse counterstamps from different dies.