Google Map's best route is I-40, I-44, I-70, I-69 to Fort Wayne, then through Detroit to Port Huron for crossing into Canada.
If it were me, in Michigan I would stay on I-69 all the way through Lansing and Flint to Port Huron, avoiding Detroit. (I try to avoid the congestion of large cities whenever possible.)
It is hard to avoid St. Louis, but there are good bypass routes using I-270. The southern bypass is slightly shorter than the northern. The direct route through St. Louis is two minutes shorter unless there is traffic congestion. (There is often a delay at the downtown Mississippi River bridge.)
You are the best judge on how to get from Phoenix up to I-40.