Thanks to Thomas for clearing some things, and yes, the Maltese cross as it is shown was appointed later to the Knights, but as you said...the Italian merchant who owned a hospital in Jerusalem had something that resembles it
As for the historical team, I'd leave that to Thomas Hospitaller
He seems to know his stuff, and I'm already working on a Knight's mod on ETW
Good luck with the mod btw, I'll surely download it when it's released
Ohh and on what Thomas said on flags and emblems:
Before change to red :
(I'm sure there were some earlier versions of the maltese cross, as there were crosses in rhodes)

(This is a meeting for prayer in Rhodes)

See the cross? It kind of a usual catholic cross but with 8 points, but not as slanting as the Maltese cross

After change of colour to red :
(Naval Jack and Order's flag)

Grandmaster's flag & coat of arms :

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I accidentaly found this on google, and it looks similiar to DOTS imo

And these are late-period plate armours from the Grand Armoury of Malta