The minecraft barrel has a 3 row inventory, the same as a large brewery barrel but on a one block space.
Maybe it would somehow be possible to change the minecraft barrel to only have 1 row inventory space (always or only with brews inside). Preferably without nms

I though about this but the risk of item duplication is just too high. Someone will find a way to extract items from the underlying inventory with some weird hopper construction or who knows what :/

How about this: Listen for barrels being opened, cancel the event and open a 9 or 18 slots sized custom inventory that synchronizes its contents with the underlying Vanilla inventory when it is created and closed.