Thank you, I found his deposition. I was looking in the wrong place.
Notably, he claims to have had some memory loss due to the accident, so it may be he has an unusually imperfect memory of the events. His deposition was also given in November 1913, over a year and a half after the sinking.
His iceberg drawing is not the iceberg he saw out the window. He only saw "something white" out the window. The iceberg drawing is of the nearest and largest of 4 icebergs he saw in the morning at about dawn. It was about 2 miles off from him.
Also important to this discussion is his drawing of the lavatory (http://www.titanicinquiry.org/images/lol/rheims2.gif
). On this diagram, he indicated that the top was forward. He also seemed to recall that that forward wall was full of windows.
1. It was the smoking room lavatory, but he forgot or confused the details. (The smoking room lavatory would have offered an excellent view)
2. It was the Gentleman's lavatory in forward A Deck, but either he heavily mis-remembered or the forward end of A-Deck was not finished.
3. It was the ladies' lavatory, or the end of the block which the lavatories were located in, and Mr. Rheim's didn't fully state where he was going and his times for that evening.
I think, that the only cases in which we can hold his memory as both accurate and honest is the case that either the ladies' lavatory was actually the gentlemen's lavatory and is mis-labeled on our diagrams, or that it was the gentlemen's lavatory and the cabins at the forward end of A deck were unfinished to the extent that they didn't obstruct his view outside.
I suspect that his testimony is gibberish, mangled by bad memory, passing time, conversations with other witnesses, and possibly by dreams. I think it is likely that he saw the iceberg pass by, and he drew a picture of an iceberg he saw the morning after, but his account of events is more or less useless.