I've archery hunted Kansas quite a bit - SE corner of the state.
While I've seen decent rutting activity at the beginning of November, I see more bucks roaming, traveling the creek bottoms and hedge rows quite a bit more during the middle of the November. I also think you're better off a little later on in that many of the larger bucks will travel into somewhat less familiar country looking for does. Pinchpoints and connecting hedgerows are dynamite. What I've found in KS is that deer are more apt to do what they're supposed to do. While still unpredictable, (uhhh, they ARE whitetails *L*) they seem to be a little more prone to travel predictable routes than some of the other states/provinces I've hunted - likely due to topography.
As you're well aware, the weather has a lot to do with deer activity. While it has nothing to do with the timing of the rut, it has EVERYTHING to do with deer activity and the frenzy cooler weather can bring. I've been there in the third week of November and had 80 degree temps and you'd swear there isn't a buck in the county.
I'm going to try something a little different this year in that I'm headed there for the week just prior to Halloween and, if I can't hang a tag on one then, I'm coming back in mid-November after a Manitoba hunt.
If I was looking for "the" optimal time for you, and it's JMO, I'd shun the first week of November, opting for the second or third week.