Is there any chance of getting Arma2/3 Workshop Content changed so you can download it without owning the game i.e using an anonymous account.
Basically PlayWithSix / ArmaSync / A3Launcher could be using steam workshop to download mods.
Atm there no way for a 3rd party client to download steam workshop content, without asking user for their steam username + password + steam guard key.
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Or another method is
Add a commandline switch for arma3 launcher that downloads the workshop content for you to a specific directory.