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Your present list restricts you to 2 things: An early MIAG (or very early Alkett) vehicle, and one without zimmerit. This is certainly indicative of some of the older (early 43 model) StuGs in Normandy.
But if you wanted to be more representative of mid-44 usage by LAH, you might consider a later model, at least one with interlocked hull details, 80mm hull front and schurzen, and almost certainly zimmerit. So you could update the 6320 kit with various details from the 'old' DML StuGs such as 9058 (still very good for detailing), or correct/crosskit with a Tamiya StuG for a Normandy Alkett vehicle (another good way as the Tam kit is still pretty good if a bit of a muddle timewise). And you'll need some schurzen plates, Atak zimmerit (or DIY - Alkett or MIAG type) dependent on your choice of build.
Or buy a DML 6581 (Dec 43 build) or even the Cyberhobby 6412 (May 44 build) kits if you can find one. In that case the zimmerit is a must.