It only took me a written, tanker, airbrake and hazmat way back in my time to get my CDL transferred and 20 minutes with photo and cranking out new CDL here in Arkansas from Maryland. This was a very longtime ago. Alot has changed and "Hardened" since especially 9-11.
The big thing is you are not allowed to possess more than one license so that CA or any other license must surrender to Missouri.