Why would Washington pick department heads with such differing opinions on how to run the country?

So that many people were represented and their opinions heard.

americans had many intangible advantages. well since the british fought a war far from home military orders, troops, and supplies sometimes took months to reach their destinations, and the british had an extremely difficult objective. they had to persuade the americans to give up their claims of independence, americans had a grand cause: fighting for their rights, their independence and their liberty. this cause is much more just than waging a war to deny independence.