The issue is that Safedock does not park me in the same position as I end up at when using Goto Airport through the FSX menu.
Sorry, but I haven't explained it very clearly: the GSX parking system, in general, WILL put the airplane in the same parking position as the Go To Airport menu, but that's only when there's no customization of any kind, which means the marshaller.
The docking system, instead, can have a generic "offset" and (for those sceneries that supports it, see my previous list), custom offsets depending on the airplane type.
The generic offset is correct for the A321, and I tried the default A321 in one of the gates you reported, E52, and the airplane ends up positioned correctly, with GSX recognizing the airplane as parked, and the jetway moving.
So, I confirm it's just a matter of adding the different offset depending on airplane type, which is a feature not used in LSZH. It's not really difficult, so you can expect a quick fix.