OK, I'll say it.... yes, it is too narrow.
Once you flip down the perches to open the nests, it will be even narrower.
I say this with surety because I too dealt with a narrow coop space and mine is 6' wide
Where is the roost?
....and how will they get down from the roost(or that upper nest)without the room to fly down....adding a ramp would take up alot of room) ?
Trying to think how to make that space work......
Maybe if you could put that nest bank on the other side of that divider wall (on the left of pic) and cut holes in the wall to access nests......
.....you only need the bottom row of nests, so that eliminates that height problem.
Ladder roosts along short end of far wall, keeps the poopiest area out of the walking path, they can hop down ladder to get down....would take up about 4 feet of floor space tho.
You could probably build some slim line feed and water devices into the wall on the left too.
It's still pretty small for the winter confinement of 6 chickens, I'd never put 12 in there.