Tracking box to full viewport
Tracking the corners of the screen isn't the same as stabilising the image. 
Whatever you do, the stabilisation is going to reduce the overall resolution of the video, as it is going to have to scale up to fill the viewport with the cropped stabilised image. 

Here's a YouTube tutorial showing how to use image stabilisation in AE:


                
            

LockNLoad is a plugin that can help with stabilisation, but it will still make the image look softer. 

Alternatively Final Cut has stabilisation built in too. 
The best option would be to reshoot with the camera on a firm surface, and avoid the wobbles in the first place.