Agreed! This is a real pain for me living in the Sierra Nevada Mountains where temps get really cold then a trip off the mountain to warmer climate creates a lot of pressure changes. I've had low tire pressure warnings in the mornings and it usually goes off by the time it warms up or I go down the hill. It I top them off cold by the time I'm off the hill they are over inflated at times, so it's a constant juggle. Just try to find the happy medium. Mileage and tire wear come to mind.
I do not have your problem of extreme temperature swings in the middle Midwest, especially in the same day during one drive. I usually run my tires at 35 as a compromise especially in fall as colder weather approaches. Keeps me out of the under-inflated situation which can be dangerous, especially at higher speeds. That alone can be a big issue in shortened tire life, by heating up the tire.
I have to pump up my PSI when I tow even during the summer depending on weight. Its not unusual that I keep my tires at 35-36 all summer.
The other factor is the door PSI is the recommendation as a compromise between ride, mpg, tire wear by the manufacturer. Your actual PSI will be based on conditions, mainly load on the tires. For most the door is best to follow.
In my opinion it is much better running 2-3 lbs over than 2-3 under. Over inflated produce less heat on the tire and longer life. More heat on the tire will actually damage the tire itself as heat is the enemy of a tire. Even running at 40 will not hurt the tire, but will give you a bumpier ride, a traction difference for the tires, and probably some extra wear. That is unless you have a very heavy load on the rear.
In theory you could go to the max psi cold on the sidewall and be OK but would likely make the vehicle unstable, unless loaded.
So you do have some flexibility in your psi settings beyond the door listing.
I hear that the snow will be around till the 4th of July in the Sierra Nevada this year. But still you have a beautiful place to live.