I've just received the burial records of the Cathedral Cemetery ("CC") and can clear some things up.
For clarity, I am referring to John Patrick Stephenson (b. 1850) as John, Sr., and his son as John Jr. I am basing this on all of the information that you have uncovered as well as my work at Ancestry and the cemetery records. For the sake of brevity, I've omitted the citations. I have provided the information received from the Cathedral Cemetery at the end.
John Stephenson, Sr. was born in 1850 and died on September 26, 1924. He was interred on September 26, 1924. He emigrated to the United States in 1866. He married Mary Spearing in 1871. By way of confirmation, Ellen Spearing (b. 1854; d. 1938) is also buried in the plot, Everyone else is a Stephenson, and I was informed that she was Mary's sister. Also by way of confirmation, in 1920, John Sr. or Jr. reported John Sr.'s birthdate as about 1840 and his immigration date as about 1860.
Mary Spearing Stephenson was born on February 2, 1841. Based on her death certificate, she died on June 17, 1908 and was interred on June 20, 1920. Her DOB appears in her death certificate. At the time of Mary's death, John and she lived at 2521 Olive Street. At the time of John Sr.'s death, he lived at 2518 Meredith Street. At the time of his death, the Cathedral Cemetery recorded his age as 74, making his DOB to be 1850.
In addition to the four sons that we know about, John Sr. and Mary had two children that did not survive.
Joseph was born in 1876. He died in 1888. At the time, John and Mary Stephenson lived at 265 Bagoda Street, Philadelphia.
Mary Stephenson was born on in 1877. She died on January 18, 1892. At the time, they lived at 844 Bambrey Street.
John P Stephenson (Jr.) was born in 1872 and died in 1946. He married Mary Fee, who was born in 1875 and died in 1938. They resided at 2518 Meredith Street together until 1938. John remained there until his death. His widow, Agnes Fee Russell, remained there until her death in 1976.
I am going to do a more detailed summary that links each of these facts to its citation but I wanted to share with you how much we have achieved. Gadget, Aghadowey, Radcliff and Heywood - you are masters at this and I am very grateful for your help.
Best wishes all.
Mark
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Cathedral Cemetery
Joseph Stephenson, age 12, interred 12-15-1888
Mary Stephenson, age 15, interred 1-18-1892
Agnes Stephenson, age 92, 8-28-1976
Mary Stephenson, age 67, 6-20-1908
John Stephenson, age 74, 9-26-1924
Ellen Spearing, age 75, interred 6-2-1938
Mary Stephenson, age 62, interred 12-29-1937
John Stephenson, age 74, 11-13-1946