The end of a port which gets the DD pressure from the valve body goes thru the front pump and then thru either a combination of gaps in bushings, shafts or thru a gap between rotor teeth finally ending at a hole in the side of the input shaft. The exact route thru the pump depends on parts combinations. The input shaft is bored down the middle and that passage ends behind the DD piston. Pressure goes thru the various gaps and spaces at the pump, forward thru the input shaft and exits at the DD piston.
When the DD clutch comes in to take the load there is not much need for the turbines so when the clutch applies, the oil circulation inside the converter pump and turbines is reduced allowing the piston to more easily move. To release the DD clutch the pressure behind the piston is dropped and simultaneously the fluid under some pressure begins to start circulating thru the converter again. The loss of pressure behind the piston and the increased flow in the converter pushes the piston back freeing the clutch plate.
Before you take the converter apart you might check first to see if your transmission has had the front pump or rotors replaced and might be one where the combination of new pump rotors and the existing converter pump shaft was one where a restriction in the path to apply DD pressure might occur. There was a service article outlining a particular combination of parts that needed some extra work done if it was put into service.
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