Shipbucket

JOHNSTON was one of the "square bridge" FLETCHER class destroyers, which incorporated a revised/simplified open bridge based on British war experience.

General Arrangement of the Bridge Area (pp. 49-50)
The arrangement of the bridge was a controversial matter. The design approved by [SECNAV]... was similar to the square-bridge configuration of the modified Fletchers... it was changed to an arrangement referred to as the British-style bridge.
...
In British practice, the conning officer's position was in an open bridge above the pilothouse and helm...
...
Both of the British-style bridge configurations were immediately unpopular with most of the ships' captains...
...
After considerable effort, the draftsmen... created a new bridge. The arrangement was similar to the square bridge of the modified Fletchers...

The usual excellence I've come to expect. While it's certainly true that British experience went into the bridge revisions, this seems to sort of invert the design process. I am away from a scanner today, but these are some selected quotes from Sumrall's "Sumner-Gearing-Class Destroyers", which is probably the bible of the latter classes.

My own selection of quote snippets is borne out of laziness, and I'd be happy to scan a few pages to clarify if you think I'm presenting the wrong interpretation. As I read it, the bridge you've drawn is the quite traditional American approach, without the semi-plated-in upper level for the OOD that the British seemed to prefer.