Bayshore
My Dad has the modern bascule bridge and I have the Traiman High cube and Weaver B&O wagon top. However, the bridge is packed away and I have not run those cars through the bridge. And I can't find the internal dimensions of the bridge on line.
Perhaps some others here can confirm my guesses. The Weaver B&O wagon to box cars should be fine. The height is similar to any other late 1930s box car like the Milwaukee rib sides, the 1937 AAR design or post war cars like the PS-1 and the Trainman standard 40 foot box car. The Trainman high cube might be trouble. It is a scale model of 1960s era cars that were much taller than a standard box car.
As a tangential but fun factoid: Forty foot high cube box cars were frequently used in appliance service. The Atlas Trainman CB&Q high cube includes prototypical instructions that the car is to be returned to Galesburg, Ill when empty. Galesburg was home to the Admiral appliance factory.