Certainly you should be getting a faster speed than that. It's nothing to do with any initialisation period, because the router will always connect at the best speed it can, right from the start. And it's not to do with your IP profile, because this is controlled by your router's connection speed, not the other way about.
What seems to be the problem is that there's no bit loading above tone 100 or thereabouts, which suggests some considerable interference in the higher frequencies. To trace this, the first thing to do is to remove the master socket faceplate and connect the router to the test socket inside. This isolates all your internal extension wiring, so if the sync speed is still low you can be pretty sure that the problem is external.