Does the N3 socket/connector provide any advantage over the E3 counterpart or is it just a way to differentiate the more expensive cameras from the other ones and possibly make customers pay for the remote triggers twice?
There is no essential difference between the two types of connections other than the shape and arrangement of the connectors. The N3 socket on the camera body is probably easier to make weather sealed than the E3 socket that is basically a 2.5mm stereo mini jack. Both have three wires: a ground, a half press, and a full press.
Amazon once sold such an adapter in the U.S., but it is no longer available. However, many of the third party accessories that are available with one connector are also available with the other and are usually fairly cheap. There's even a TC80N3 knockoff that comes with adapters for almost every imaginable camera that uses the basic three wire shutter release.