Here's a great resource for all things Katy Trail: bikekatytrail.com
The Rock Island Trail is years from being finished.
I've ridden across Missouri a few times on roads. I'd go the northern route as it's flatter.
If you want a supported ride, this one is hard to beat. I've done it the last 5 years and plan to do it again this year. Make sure to sign up on March 1st as it's been known to fill up in as little as one day!
https://mostateparks.com/2016KTRide