High Street presently exists only between Pearl Street and Jay Street, entirely to the east of the station bearing that name. At the time the station opened in 1933 however, High Street extended between Fulton Street (now Cadman Plaza West) and Navy Street. It has all since been removed. Another segment exists between Cadman Plaza East (formerly Washington Street) and Adams Street southbound, directly above the station, but this has been renamed Red Cross Place.
Septa has an oddity like that with a trackless route, there is a short turn loop for the 66-Frankford Ave. line, at Gregg St. Gregg St. does not exist at Frankford Ave. anymore, it can be found further west, IIRC.
Looking at current and historic maps and aerial photos, I think Red Cross Place is actually slightly north of the old High Street.
I think where High Street once was is now the parking lot of the NYC Emergency Management building.
The digital tax maps do not show an ROW under that that, but matching up the ROW to the East and West, it seems like it would go just south of Red Cross Place.
Looking at maps.nyc.gov and turning on the transit layer (which is usually by not always correct), the line goes through the parking lot.
The MTA Neighborhood map (which is usually correct) also shows the station just south of Red Cross Place.
Modern aerial photos show the two streets (RC Place and High St) to be not aligned, so you appear correct. Tellingly, there are no buildings with old facades along RC Place which might indicate an ancient street. There is an NYCTA building on the north side with bricked up arches, but it is not clear if it was ever mid-block. It does extend north to the former Sands Street.
Another bit of proff for your theory is that the Adams Street entrance is set back from RC Place, where it would have been on the south side of the old High Street.
I think the building is the proof that the RC Place is north of High.
In the 1951 view you can see the shape of the NYCTA building, with another building to the south, and then High Street. The NYCTA building apparently faced Sands street to the North.
One more piece of evidence that Red Cross Place is not the former High Street: the 1916 Brooklyn Atlas Shows the building "Rapid Transit Sub Sta" ending a bit over 100 feet north of High Street (I think the dimension on the lot to the south is 106.2, but it is not entirely clear).
Compare to the Google Street View that shows the same shaped building going almost to the sidewalk of Red Cross Place.