I found the drawing of T.C.R.L. 108. It shows the right side. The photo of 109 shows the left side. The car numbering implies they're in a series. Maybe.
Anyway, if I'm seeing both sides of the car, then the doors are indeed NOT aligned across the car. And, since there's no ice hatch showing to the right in the photograph, that implies there's only two ice hatches per car. And that they're on opposite corners of the car. Which gets me thinking that to ice both ends of the car, the "icers" would have to get the ice slid over to the opposite side of the car for one of the bunkers. Quell irritating!
As a final check, if anyone can find the cars' info in ORER's (I found nothing in 1926), I would appreciate it being posted here.