Your airlock idea sounds extra fussy, actually. I think when you consider the sheer magnitude of stuff that needs to move back and forth you'll have trouble. Many fortresses run into barrel shortages. You'll have barrels split between the two fortresses, presumably men making them, but women usually filling them and returning them to the men full of booze and needing to be returned. With a large fortress, it's a LOT of moving.
Two ideas:
1) Create a shaft from one fortress to the other and a 2nd working in reverse. Put a stockpile at the top of the shaft for items to move to the other fortress and periodically designated it for dumping and unforbid the dumped items at the bottom.
2) Create shared stockpiles that are connected to each fortress but use a double floodgate design to ensure that only one fortress can access it at any time. A lever in one fortress opens one floodgate on the local side and closes one on the remote side, a lever in the other fortress does the same. Only when both levers are thrown can access shift from one fortress to another. If you create two that hold the same items (say booze), one can always be accessible to each fortress, so both production and consumption can be satisfied.
The second case would probably work best, particularly for moving a lot of mixed item types (food, booze, barrels, bags, stone). Use other stockpiles within the fortress set to take from/put to the airlock stockpiles to automatically empty/fill the airlocks when you switch rooms.