It’s tricky, because you don’t want to drive the former loyalists into one another’s arms and create an anti-regime coalition.
The long-term play is to balance carrots and sticks, to give these houses just enough reasons to stay loyal while simultaneously weakening them in the long run. So instead of sending Mathis to the Wall, I’d order him to pay for a new royal navy, while offering temporary concessions on wine excise tax. And so on.