Thanks, everyone, for all your help. It sounds like this drive will be pretty straightforward. I personally love the closed-ticket system, so the Kansas Turnpike will be a breeze.
Regarding our drive through Oklahoma, yes, we will be taking both the Turner and Will Rogers Turnpikes (I forgot to mention the Will Rogers before). I will just stay on I-44 the entire time through the Tulsa area. (As much as I'd enjoy driving through I-244 in downtown Tulsa, I'll have to save that for another trip.
Sunday, July 8 will be the day we pass through Oklahoma, so there won't be any concern of rush-hour traffic at all. That's the day we will be driving from Amarillo TX to Springfield MO. I figure we'll probably be lunching in the Oklahoma City area. :-)
Thanks again for your help!