Etymology of English "Achoo" relative to other sneezing onomatopoeiae

So I was recently curious about the sound that people sneeze with in other languages and was surprised to notice the difference between the English onomatopoetic word "Achoo" and that of other languages in the same family. For example:

German - hatschi

Dutch - hatsjie

However some of our sibling languages are closer:

Icelandic - atsjú

Norwegian - aatsjoo

Interestingly, most of the world seems to pronounce their sneeze more like modern Germans than modern Americans (basically all of Eastern Europe, Russia and Asia will end their sneezes with a short i instead of a long o).

Does anyone have any ideas why the pronunciation differs between ending in a short i in many closely related languages and a long o in English? Presumably people talked and wrote about sneezing relatively early on before these languages broke up so there should be some sort of proto-English pronunciation that either split during a period when most of these branches hadn't extended far, or English changed its common representation of the sneeze at some point in history. Does anyone know of a time in English's history when our sneezes ended in 'i' or a time in German/Dutch history when the 'oo' was favored?

Note that the OED traces the word back to the early 19th century, always spelled ending in the 'oo' sound and not a short 'i':

Forms: α. 18–19 aitchoo, 18– achew, 18– achoo, 18– ahchew, 19 ahschoo, 19 ahshoo, 19– ahchoo, 19– atchoo, 20– aitshoo.

β. 19 achoos.

I think the reason that you find predominantly two major forms for sneezing (ending in [i:] and [u:] may be because most sneezes sound more or less like one of those two.

I can vividly imagine a sneeze with either sound, so I find it very likely that the common onomatopoeias are reflecting that variation. Bear in mind that the Dutch and German examples that you quote are indeed incomplete, as the link form the comments shows:

In Dutch, Hatsjoe!, Hatsjie! In German, Hatschi!, Hatschu!

You mention a short [i] sound, but I think in most cases, the [i] sound is actually long a [i:]. The 18c spelling variations you quote from the OED, 18– achew, 18– ahchew, I would actually pronounce closer to an [i:] sound than the [u:] you mention.

In Dutch, the choice for ie ([i:]) or oe ([u:]) depends largely on the kind of sneeze... the [i:] will be more associated with a higher-pitched, possible restrained, nasal sound, whereas the [u:] would indicate a more unrestrained, lower-pitched, possible open-mouthed sneeze.
If someone describes a sneeze in Dutch as hatsjie, I can't help but thinking of a child or child-like sneeze, or actually a kitten (kittens never sneeze with [u:]!) Describe a big man, and I expect a hatsjoe.

Especially the last part is — obviously — subjective, but I think the general reason for the different onomatopoeias is the actual difference in sneezes.

During the 19th century, "achee" was also used for the sound of a sneeze. The earliest citation the OED has is 1843 for a-chew. And here we have earlier and simultaneous uses of atchi and atchee. Google books search shows that atchee continued being used into the last half of the 19th century.

1826:

Enter Tallboy, sneezing.
Tall. Atchi ! — here — here— Chi — chi — here, sir.
Bar. The fellow will sneeze his head off.
Tall. I've sneez'd above fif—flf—fif— atchi— fifty times in a minute. It has shook— shook — shook — Atchi ! Oh ! shook me to pieces.

1843

"Doctor", said the Alderman, "I am very glad to see you. This is — atchee ! — a matter to be looked into. It seems that — atchee ! — these nine — atchee ! atchee ! — This is very strange — atchee ! atchee ! — very strange snuff, after all — atchee ! atchee ! atchee ! — "