Your best chance of encountering other riders is to meet people going the other way (i.e., east to west). The peak time for people leaving Yorktown and heading west is the first half of May. It takes most people about two weeks to reach Springfield, KY.
If you want to meet people going west, I'd leave Springfield going east around May 20. Be aware, however, that many of these cyclists will be staying overnight at places that are less available to you with an RV, such as churches, fire stations, city parks, private homes, hostels. But you'll still see plenty out on the road.
On the other hand, if you are looking to ride with people, you'll need to meet people going east. Eastbound TransAm cyclists aren't going to show up in numbers until August. So if this is your goal. I'd wait until about August 10.