At the time, the western border of the city roughly coincided with Eighth Street. The area beyond that would have still been part of Springwells Township, and was excluded from the document. Just over the border was the Woodbridge Farm, which wasn't legally subdivided into individual building lots until 1858.
Until now, I have only had access to low-resolution images of the Hart map. But I recently noticed that the Detroit Historical Society has a copy of this map in their online archives, and a high-resolution version available to paid members. Below is a detail of the area including Corktown.
Image courtesy Detroit Historical Society.
Superimposing this map over a modern aerial photograph can help researchers determine which structures in Corktown were built before 1853.
The houses that I believe coincide with existent structures are highlighted in yellow. Some buildings appear to coincide with the 1853 map, but they are known to have been built afterward. For example, today's Most Holy Trinity Church was built after the older wooden structure was demolished in June 1856.
Of the small handful of houses in Detroit that predate the publication of Hart's map, these seven can be found in Corktown.