Lithgow as Churchill? You must be joking!

The series is excellent: all of the various characters are, I think, astonishingly similar in appearance to the people they are playing.
All, except the amazing and incomprehensible choice of Lithgow to play Churchill.
Anyone who has seen any of the films, TV series or documentaries of and about Churchill would recognize right away the difference in height (Lithgow 6'3" vs. Churchill 5'6" at that age), as well as the posture. Lithgow comports himself as a caricature of the top-hatted fellow in The Yellow Submarine--and he looks every bit as soul-threatening as that character.
I have admired Lithgow's performances over the years, in drama as much as comedy--but I cannot understand why:
1: the producers would ignore the wonderful British actors imminently capable of portraying a truer version of the man, and
2: why Lithgow himself would even consider accepting the role--beyond a momentary feeling, perhaps, of the lovely compliment paid to him by the offer itself. Surely common sense would have dictated the answer?
What were they all thinking?
Though I follow the series closely, and occasionally, out of interest, check some of the imputed facts, I have to look away from every scene which so misrepresents the character of how Churchill held himself, how he spoke etc.
I do not idolize Churchill--I have studied him, and history, for too long, not to recognize that how he saved Britain (and, by extension, the entire western world) was not through any military genius (as he liked to posture himself), but by sheer bluster and bravado. Thank God for that--for his mucking about with the military could easily have put an end to the whole show, as has been adequately illustrated by many historians and his closest contemporaries.
Sorry, John: but there it is.