Some facts for those still following this saga . . .
Thorn has it mostly right regarding the pin/pendant/medal/badge (period papers refer to them as medals or badges). The initial plan was for only the "winning" umpire to receive a medal but that changed. There was Honest John Gaffney for NL and Honest John Kelly for AA. The two-umpire system worked great and would be used with increased frequency in later years. With Detroit winning the World Championship, Gaffney was by extension the "winning" umpire however both would receive a medal.
The team "members" received their badges on October 21st of 1887. The badges featured a batter as a central figure while in April of 1888 the umpires, Gaffney and Kelly, would receive badges of a slightly different design. A great description of the umpire badges can be found below (see the Kelly writeup).
The players, as mentioned, received their badges on October 21st (after game 11, 2nd game of double header) while still on the East coast which was convenient for Helen Dauvray. The final games would head back to the mid-west (Detroit, Chicago, & St. Louis) to finish out the 15-game series.
Lady Baldwin Medal (not mine)
There were exactly 14 Detroit players to collect stats during the World Championship as follows:
Lady Baldwin
Charlie Bennett
Dan Brouthers
Pete Conway
Fred Dunlap
Charlie Ganzel
Pretzels Getzien
Ned Hanlon
Hardy Richardson
Jack Rowe
Sy Sutcliffe (final 3 games only)
Sam Thompson
Larry Twitchell
Deacon White
However, I don't believe Sy Sutcliffe would have been awarded a medal as he joined the team later, collecting his first Detroit AB in game 13. That 14th badge could have been awarded to manager Bill Watkins. Chris Von der Ahe of St. Louis and Bill Watkins of Detroit were both very well known. I wouldn't be surprised if Helen Dauvray opted to gift medals to the winning manager as well. I note that some accounts refer to the "members" of the winning team vs the "players" as the medal recipients. I suspect a deeper dive might shed further light on this possibility.
I personally like this painting but would need to be assured that if I find it to be a modern creation or the medal a modern addition that a full refund is waiting. Deciding which team member the painting represents is far from settled and open for debate. Unfortunately, none of the listed possibilities in this thread are a strong match. Sam Thompson, Bill Watkins, and a few others are in play. If authentic, I also think it possible that a family member or friend of a player could have worn this pin.