Imperial Family Handwriting.

One thing strikes me as odd - the handwriting on the replies in French to the notes supposedly delivered to the IF during captivity in Ekaterinburg from an 'officer', implying potential escape attempts, do not match any of the handwriting samples known to be from any member of the primary Imperial Family - ie Nicholas, Alix or the children. So, who wrote the replies?

The replies written in French coming from the Romanov floor are generally thought to  have beenwritten by Olga, though not composed by her. Maybe her handwriting was simply the best. If the  (Romanov)replies to the rescue letters are extant a comparison to known samples of Olga's handwriting would confirm or eliminate her. Not sure, but I think at least one reply letter survives, possibly in GARF.

[Mathematic, art and history in ♥]

The replies written in French coming from the Romanov floor are generally thought to  have beenwritten by Olga, though not composed by her. Maybe her handwriting was simply the best. If the  (Romanov)replies to the rescue letters are extant a comparison to known samples of Olga's handwriting would confirm or eliminate her. Not sure, but I think at least one reply letter survives, possibly in GARF.

I think that all four letter survived, at least, copied. It is believed that Olga Nicholaievna had written the letters, since her French and handwriting was the nicest, she was dictated what to write. Of course, if she indeed was the one who wrote the letters.

You can see photos of the IF's replies to the officer letters on pages 313-14 and 318-19 of Fall of the Romanovs.

The writing is much more careful and deliberate than most samples of Olga's notes and letters that have survived, but the style and construction of the letters does indeed match Olga's handwriting.

This is basically a bump of this topic and actually more specifically of the topic "Has anyone ever seen "OTMA' written out by an Imperial Family member or someone of their time?"
 I think I have, sort of. In the Russian language book Tsesarevich by Olga Barkovets about Tsarevich Alexei  on page 142 (and  elsewhere) Alexei,in a July 12, 1916 diary entry, refers to "Mama (and) O., T., M., (and) A." This is not exactly "OTMA" as a collective name for his sisters , but when viewed on the page it really does seem  like the acronym OTMA we all are familiar with. And it's used in the same way ,to save the effort of writing twenty-five letters (Olga, Tatiana,Maria, and Anastasia) when it could be done with four.

He does the same in a diary entry of January 2,1916.

This makes sense and I would say it's really very similar to the standard OTMA acronym.

This is basically a bump of this topic and actually more specifically of the topic "Has anyone ever seen "OTMA' written out by an Imperial Family member or someone of their time?"
 I think I have, sort of. In the Russian language book Tsesarevich by Olga Barkovets about Tsarevich Alexei  on page 142 (and  elsewhere) Alexei,in a July 12, 1916 diary entry, refers to "Mama (and) O., T., M., (and) A." This is not exactly "OTMA" as a collective name for his sisters , but when viewed on the page it really does seem  like the acronym OTMA we all are familiar with. And it's used in the same way ,to save the effort of writing twenty-five letters (Olga, Tatiana,Maria, and Anastasia) when it could be done with four.

He does the same in a diary entry of January 2,1916.

This makes sense and I would say it's really very similar to the standard OTMA acronym.

IMO, it's not similar enough to prove Gilliard's claim -- particularly since Aleksei uses "и" ("and") to separate Maria and Anastasia's initials. Throughout the family's diaries you'll find similar abbreviations, but here's always a deliberate use of punctuation, which, to my mind, denotes an abbreviation rather than an acronym or the alleged "Otma" composite Gilliard claimed they used.

Well, Alexei's usage is using initials, it's true. And he used a period after each initial because that's proper punctuation after an abbreviation of even a single letter. I wouldn't  make too much of the difference between W, X, Y,& Z, and W,X,Y,Z.   We say USA, after all, not USofA(well, most of us don't).
In the case of a diary entry, the four letters of his sisters' names serve to name the sisters. The same as the acronym OTMA does for both its writers and readers. So, you're technically right ; it's not the usual acronym. But Alexei's usage serves the exact purpose as the acronym , namely brevity, and except for the periods, is an acronym. But true, it doesn't support Gilliard's contention of OTMA being a well known acronym for the GDs. It does lend credence to the desire to have an acronym for four girls so often together and thought of collectively.

I know it sounds like I'm splitting hairs. I'm a fussy person when it comes to this kind of thing.

Gilliard claimed the girls used "Otma" as a "composite Christian name" -- not an acronym or abbreviation. That's why I pay so much attention to capitalization and punctuation. To my mind there's a significant difference between using an abbreviation and adopting a collective identity.