I can see a *possible* solution. I'm not 100% convinced but there are a lot of similarities!
We can see Webb Short on only one census:
1910 US Census
663, Grand Street, Brooklyn, Kings, New York, USA
SHORT, Webb, Head, 45, Married, born New York, Stone Cutter
SHORT, Clarence, Son, 4, Single, born New York
So, looking for other Shorts in the area produces one interesting individual. and I think the "Webb" Short and "Sylvester" Short may be the same person???? Perhaps he didn't like the name Sylvester?
1905 New York Census
161, Union Avenue, Brooklyn, Kings, New York, USA
SHORT, Sylvester, Head, 41, Stone Cutter
SHORT, Annie, Wife, 30, Housework
SHORT, Charles E, Son, 15
SHORT, Clarence E, *Daughter*, 10 months
but "daughter" could be an error by the enumerator? I've never seen Clarence used as a girl's name before?
1900 US Census
379, South 2nd Street, Brooklyn, Kings, New York, USA
SHORT, Sylvester, Head, 36, born New York, Stone Cutter
SHORT, Annie, Wife, 24, born New York,
SHORT, Charles, Son, 7, born New York, at school
(This census gives "Number of year married" as 11, making Annie 13 at the time!)
I can't find Sylvester, Annie or Charles on the 1910 US census!
(Sylvester can be traced back in earlier censuses to the Short family I mention in Saugerties, up the Hudson River!)
There is a death for an Annie Short in King's, New York on 22 Jan 1910, aged 35.
So the "Webb" and Clarence on the 1910 census would fit!
Also, Union Avenue, South 2nd Street and Grand Street are all in the same part of Brooklyn!
There is a death for a Sylvester Short in Queen's New York on 23 Jan 1915, aged 50.
This would explain why Clarence was in an orphanage in 1915 and 1920?
Of course, without sources this is all conjecture! You would need to get hold of birth and death records from the New York City Department of Records.