If Oswald used the front staircase as you say, and then enters the Break Room 10 seconds ahead of Officer Baker, how would Baker see him through that small window on the door leading to the Vestibule? (As testified to by Baker). Do you generally believe the Baker story of seeing Oswald through that Vestibule door window is BS?
Its a question of timing. Since both Baker/Truly and Oswald would be in proximity in a 10 sec range of time, its not inconceivable that opening the door, closing the door would cause some kind of change in light intensity streaming thru the 2 windows.
But the Geneva Hine in the hallway as early as 40 sec post shots, kind of conflicts badly with an up the front staircase from front lobby trek by Oswald, imo.
Right now, the Prayer person being Sarah Staunton, one has to wonder why Staunton being a 400 lb obstacle in the way of the oncoming Baker, would not remember having to move out of the way of, nor see Baker, or vis versa, Baker having not mentioned either.
Since there are these people in proximity , then the storage room option for Oswald
becomes ever more probable than the other 2 options, Domino room or going up to 2nd floor lunchroom, because of being in LOS of others like perhaps Joe Molina, for not more than about 5 secs, before disappearing out of LOS again.
Oswald puts on his jacket while still in the storage room, and exits, and possibly even surprised Baker who is following Truly, across the lobby, about to reach the 2nd set of glass doors.