Twelve years ago we set off on our very first RV trip with our 34' 5er in April. It ran from Austin TX to the Eastern Shore of the Chesapeake Bay, MD.
Not being familiar with tornados we had the same apprehensions as you about travelling through the midwest during tornado season. We did have many years living at home in Bermuda & dealing with hurricanes. You can dodge a thunderstorm if you are on the move. You cannot dodge a hurricane when you live on an island.
Many years & miles later we keep a very careful eye on the weather. An easy thing to do these days. If you are in a CG, that is where you are. There is no dodging whatever is coming your way.
We have dodge a couple of severe thunderstorms. First one, before we had a smartphone, with the help of a ham radio operator in Dodge City, KS. We had a severe TS coming up behind us. Online he could see the track of the storm & gave us a detour that took us out of its path. Another time, while travelling east on hwy2 in MN we had a storm also travelling east right behind us like a train on tracks. In that case we turned north on a highway, went about 10 miles of so, stopped & watched the storm roar by to our south, went back south & continued east BEHIND the storm.
Chances of even being in a tornado warning area are somewhat slim. Be aware before the severe weather hits. Like dealing with hurricanes, running around outside preparing for a storm that is already ontop of you is too late.