A 'writer' is indeed one of the tasks of a solicitor's office - not necessarily a 'writer to the signet' - usually denoted as 'WS', which is a law library in Edinburgh. It does appear that these 'Warrant' marriages, by and large are/were performed in commercial properties, usually solicitor's offices.
Regarding 473 St Vincent Street, I recall this area in the 1950's, and it is a red sandstone property (a standard tenement). Once St.V crosses North Street (where the M8 now passes) commercial properties gave way to high density housing, usually with shops/pubs on the ground floor front, with 2 room houses to the rear ground, and 4 room houses on the upper floors.