Welcome to KC! That's where I've lived for a couple of years, and I've flown that route a few times on US Airways.

First off, what is your list of preferred carriers? If United is one of them, you could continue with MCI-CLT-RDU as you normally would. If you are concerned about US going under, you could begin accruing UA miles/status, and just switch over to MCI-ORD-RDU or MCI-DCA-RDU (assuming UX keeps that route). You'd never have to go through a painful period of reacquiring status.

For duration, Delta is the best bet with connections through ATL - gate-to-gate in about four hours.

I personally like American at MCI - no RJs, frequent flights to both DFW and ORD, and I generally get the upgrades I want as a Gold or Plat. No fare restrictions on upgrades and you earn full miles on any fare. Only downside with RDU is that gate-to-gate is usually closer to 5 hours. So you're leaving 45 minutes or so each way on the table vs. DL through ATL.

There is no longer a Southwest advantage on this route (although there once was) - they are now one-stop through somewhere and are no faster gate-to-gate than Delta. If you already love 'em, then they are as good an option as any. But if you don't, rest assured you aren't missing out on nonstops in your quest for Big Six miles.