It's only right that we put a gangly, whimsical monarch who loves ridiculous hats in the place of a gangly, whimsical Time Lord who loves ridiculous hats- and anyway, who else would call their time machine 'Sexy'? Naturally Sotherby gets dragged along on timey-wimey adventures.
Charles II/Sotherby, Doctor!Charles and companion!Sotherby
Bonus points for mentioning K-9? Affirmative!