We have been to St Louis several times and this is what we have done.
From Chandler to Dancing Eagle Casino RV Park overnight with hookups $10.00 and 366 miles going thru Payson to Holbrook to get to I 40
From Dancing Eagle either Oasis RV Resort Amarillo 326 miles if you have the time spend a couple of days camping at the bottom of Palo Duro Canyon at Palo Duro Canyon State Park.
Then 226 miles from Oasis RV is El Reno West KOA We like to make this a shorter day since we have had two 300+days and it is a fun stop.
From El Reno West KOA to Springfield / Route 66 KOA is 321 miles
From Route 66 KOA to Casino Queen RV Park in St Louis is 228 miles
and from Casino Queen RV Park to Peoria 166 miles