Using the canal locks for the Three Gorges Dam as a reference, I think 10,000 would be the limit.
Good idea of using the lock limits as a guide. But we need to remember just how deep inland the Three Geoges Damn is. The further up river, the shallower and narrower the river, so if the river at the Three Gorges Damn can take 10,000k ships, the stretches of the river near the coast should be able to take far heavier ships.
Are you guys trying to see which shipyards might be able to construct the rumoured new 10,000k cruiser class? If so I think that shipyard infrastructure and the experience and skill of the workers would be the main limiting factors as opposed to the location of the yards.