I've not been able to crack Edmond Johnson's puzzle tokens, but I wanted to write in with some additional information. I decided to first approach Johnson by way of contemporary reports of the 1893 Chicago Columbian Exposition, in the hope that there would be some mention of his tokens.

While I did not find any token references, I did find reports of Johnson's exhibits of reproductions of ancient Irish jewelry and artifacts. Later, some of his replicas of Irish antiquities were sold to a Chicago museum and ended up in the Spurlock Museum at the University of Illinois. You can see Johnson's magnificent copy of the Ardagh Chalice and other items on their website. The museum has also made available a copy of Johnson's descriptive catalog via the HathiTrust site.

Reproductions of Irish cultural icons on display at Spurlock Museum(https://news.illinois.edu/view/6367/408999)

Illustrated supplement to the descriptive catalogue published by Edmond Johnson ... of fac-simile reproductions of Irish antique art metal work(https://babel.hathitrust.org/cgi/pt?id=uiuc.7969286&seq=12)

The only newspaper mention I found about the puzzles was from the August 8, 1946, Belfast Newsletter. A reader asked for information about the token and said that it was

Since I hit a dead end with contemporary references I decided to see if I could figure out how the puzzles were meant to be solved. I've determined that these pieces are something called a As of 2020, Klaus Schmeh's website indicated that the world record for solving a Playfair Cipher without a key is 26 letters. Since both of Johnson's puzzles are 22 letters, we may have a problem!

I also came across a program that works out solutions to Playfair Ciphers. I've had some fun with it but no eureka moments so far.

Playfair cipher(https://en.wikipedia.org/wiki/Playfair_cipher)

Can you solve this Playfair cryptogram and set a new world record?(https://scienceblogs.de/klausis-krypto-kolumne/2020/01/27/can-you-solve-this-playfair-cryptogram-and-set-a-new-world-record-3/)

Playfair PH solver using Web Workers(https://bionsgadgets.appspot.com/ww_forms/playfair_ph_web_worker3.html)

To read the earlier E-Sylum articles, see:
UNSOLVED NUMISMATIC PUZZLES FROM DUBLIN(https://www.coinbooks.org/v27/esylum_v27n01a09.html)
MORE ON DUBLIN JEWELLER EDMUND JOHNSON(https://www.coinbooks.org/v27/esylum_v27n02a08.html)