I guess DeWalt has a non-standard vac port now? Most of the "shop vacs" I have come across have a vac port that the vac end of a Festool hose will fit right into. Have you tried just plugging the Festool hose into your DeWalt vac without the Dewalt quick connector.
The tool side of both connectors listed (202346, and 500668) should be the same in order to connect to Festool tool ports. The hose side of the connectors will be different in order to connect to a 27mm hose or a 22mm hose.
The D27 connector (202346) should be the right one for the hose you linked and already own. Are you certain Amazon sent the correct connector? D27 connector for the D27 hose.
It might help get a clear answer if you can post a pic showing the layout of what you are planning to connect. With a variety of hoses and connectors and ends, it can be confusing when trying to picture your planned hook up.
Seth