William Carrick...was single, living at 363 1/2 Market Street. This was known as the Elcho Lodging house and was situated opposite the Flood Building (on the corner of Powell). It was on the same block as the Call Building, near the corner of 5th Street. It seems (like much of the city) the Elcho building was lost in April 1906, during the earthquake and fire. But it doesn't look like William died in it.
I was just having another look around and noticed the address. You probably meant to type 863 1/2? I only point it out because if he was living at 363 Market, he most likely was living in a building that was built on "fill", which might have meant that if he was at home at the time of the earthquake, he could have felt the movement more severely than someone who was living in a building built on rock or at least natural soil.
During 1906, an (elderly) ancestor of my husband lived several blocks away from 863 Market and supposedly after the earthquake struck, he walked (or took a buggy, I don't remember) to where his daughter was living, to help the family. It was a two to three mile walk (depending upon where the family was living in 1906), which must have been difficult to do, given his frightening experience, seeing devastation along the way and wondering if his family members were okay. He had already been in one California earthquake; I wonder what your Mr. Carrick was thinking at the time.
If you haven't already tried this resource, I wonder if a librarian might be able to answer the question: where might those who passed away in the City and County Hospital have been buried in 1906?
They may not have an answer, but it could be worth a try? Also, if you do not live in the area, it might be worth mentioning that you cannot easily access San Francisco resources.
Library for San Francisco
http://sfpl.org/index.php?pg=2000001701