Whenever a captain steers their ship directly through the gate of ESD, it will appear in the shipyard where the Protostar is currently located. It will be visible to all captains who enter the ESD (same instance) until the next captain steers their ship through the gates... And I don't think this mechanism would be prone to bugs at all!
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However, perhaps it's more possible to have the player's own ship appear within spacedock (or out the Shipyard window at Qo'noS). Obviously, everyone would then see a different spacedock interior. (Obviously, selecting a different ship at the Selector would require an exit to space and re-enter to load it in.)
lol. During busier times it'd just be constantly flickering between ships. If it keeps the same scale and center point, every time someone docks a Borg Assimilator Dreadnought Carrier, you wouldn't be able to use the main concourse.