First of all, if you've checked any bags, forget it.
Next, while I think she'd put you on the KL flight, since it'd also have NW flight numbers to use, she might prefer to do it with someone who will just take a later DCA-DTW flight and keep it simple.
I originally had MSP-LAX-NRT in J/F, and MSP-LAX domestic portion was oversold. So I volunteered to go MSP-NRT nonstop (also in J). She had to get supervisor approval, but it was OK.
They took me, gave me $300 voucher, meals, etc.... I waited at the airport 6 hours till the nonstop to NRT, and ended up catching my original NRT-BKK flight.
Good luck!