Hi Richard, how are you? I just wanted to say congrats on the article. I thought it was very interesting. As you say, there are many layers to the "onion" of this particular mystery, and while new evidence has surprisingly continued to pop up from time-to-time, it is hard to say whether or not we will ever know the answer for certain.
Regarding Rheims, you raise some good points, but some things in his LOL deposition and his other accounts are not really clear-cut as you are aware.
I have heard both sides of the argument regarding whether the gunshots he describes hearing in his deposition are the same incident he described in the letter to his wife and other accounts or not. One thing worth considering here is that Rheims was asked if he heard any particular noises at one specific stage of the sinking during the loading of the lifeboats, to which he replied that he heard gunshots, with no real clarification or follow-up questioning from the questioners.
The main point here is that he may have been describing the same thing as in the letter to his wife, or it could be referring to another incident. There is no way of knowing for certain. The scope of the LOL hearings was regarding the liability of the White Star Line for survivor financial losses, so the question of investigating whether an officer shot anyone was really beyond the scope and purpose of the hearings. It was one of many things during the inquiries and liability hearings that I wish they had asked for the historical record.
Rheims deposition does not mention many of the details in the letter to his wife or other accounts, but then again, they didn't specifically ask him about many of those things. For example, his letter to his wife gives great detail about Joseph Loring and his last conversation with him, but he doesn't discuss this in the deposition.
Conversely, his letter to his wife and his press accounts don't have all of the details contained in the deposition. The timing of the incident he describes is hard to pin down, because he doesn't describe it in the deposition (unless the gunshots are indeed the same incident), mentions it as being while the last boat was leaving in the letter, and gives no indication of when it occurred in his press accounts, other than that it was late in the process. Which details are accurate and which aren't are hard to distinguish.
For what it's worth, I get the impression that the order of some of the sequences of events in his letter to his wife are possibly mixed or compressed, based on other accounts from him, and from his other press accounts.
What would be really interesting is if transcripts of Eugene Daly's 1915 limitation of liability testimony in the US District Court ever surfaced. Press summaries indicate that he testified under oath about the shooting incident, and his testimony might reveal more of the truth about it if it is ever found. These materials are not housed in the National Archives on Varick Street in NYC like the 1913 portion of the LOL case, and despite many researchers, myself included, searching for them, nobody has yet found them, or if they have, they haven't announced it.
Good work, and again congratulations.
All my best,
Tad