Well, it's been a while since I've been to that area, but I'll take a stab at AM. The strongest signal in the area is KWTO on 560. KURM from Rogers, Arkansas gets "runner up" status with 5kw days on 790. As for the more distant stuff, you might want to try the bigger Kansas City signals on 610, 710, and 810. They're all do-able daytime in Springfield. KRMG from Tulsa should be do-able day and night on 740...although daytime, you may get splatter from the 750 in Lebanon, MO. Back in the '90s KAAY from Little Rock used to be faint, but audible daytime on 1090. They've had a few issues since then, so I'll be a little surprised if they make it that far now. I once got the 600 and 1030 from Memphis on a car radio with a very weak signal in the Harrison area south of Branson just over the state line. You might also want to try for the Memphis 640 (which I don't think was on at that time).
I've never spent a night in the Branson area, but I've spent plenty of them in Springfield, as well as a few in Fort Smith and Rogers. The Chicago blowtorches are easy duty at night, as are "stalwarts" such as WLW, WHAS, WJR, WWL, WSM, WBAP, WHO. I seem to remember KSL blasting in one night in my hotel room in Springfield. No specific recall of either the east or west coast, however.
Happy Hunting!