I've ridden the Katy Trail end-to-end 8 times so far. If you were thinking about doing the ride in June, I'd suggest the Katy Trail Ride (
https://mostateparks.com/2019ktride). Signups start March 1st and sometimes fills up quickly.
1. Take the gravel bike. I've ridden it on a hybrid, touring bike, and road bike (for a short distance). Both the hybird and touring bikes had 700x32 tires which were adequate. However I just bought a grave bike with 650x47 tires and looking forward to the nicer ride.
2. The first 160 miles or so is flat as can be. Out of Boonville it gets somewhat hilly but only rails-to-trail hilly with only a couple of places near 5% grade. Going from east-to-west the wind can be a problem.
3. I've always taken 5 days and it's a pretty relaxing ride at that rate. I'd recommend staying at Boonville and Sedalia even though that makes for somewhat short 35 mile days but that's in the 'hilly' area.
4. Here's an excellent resource for both the Katy and Rock Island trails. Lots of info about lodging, food, etc. The forum has a lot of updated info of what's open and closed.
https://bikekatytrail.com/default.aspx
5. Speaking of open and closed, a lot of places on the trail aren't open on Mondays and Tuesdays. You might want to start your adventure on Wednesday.
6. It can be HOT in August in Missouri so bring plenty of liquids. Usually there's a trail-head about every 15 miles but not all of them have fluids.
Obviously I like the Katy Trail, but so does about everyone else that I've talked to who have ridden it.