I tried a different (lazy) way, which was to create another grid that occupies the same space as the TabControl, ie both are in Grid.Row=0. I have bound the grid height to the height of the first tab so if the tabs change height the other controls will remain centered. I set MinWidth on the window so the controls dont overlap the tabs.
Paste this code into a new WPF Window...
My Text
...and you will get this:
