David Skinner let me know that researchers have found another possible death date for Heavy Johnson: March 13, 1962, again in Cleveland. I checked this out, and found this record, in the U.S. Veterans’ Gravesites database:
Name: Oscar Johnson
Born: November 5, 1896
Died: March 13, 1962
Service Start Date: September 17, 1917
Buried in: Beverly National Cemetery, Beverly, New Jersey
The birthdate, of course, is similar to the birthdate found in the SSDI (November 2, 1896), though there it is coupled with a completely different death date (January 1964). The service start date, September 17, 1917, is well after Heavy Johnson is known to have served in the 25th Infantry in Hawaii (beginning at least in October, 1915), and conflicts with the service record I found that puts his enlistment on December 10, 1913. And finally, this Oscar Johnson is buried in New Jersey. If Heavy Johnson passed away in Cleveland, it seems unlikely that he would have been shipped to New Jersey for burial (there certainly would have been more convenient national cemeteries); in addition, Heavy Johnson has no known connection to New Jersey.
It turns out that a World War I draft card exists for an Oscar Johnson born on November 5, 1896 (Heavy Johnson, of course, would not have had to register for the draft):
He was from Philadelphia, his father was a Swedish immigrant, and his race is recorded as white.