Thanks
The wheel is otherwise good, so I want to keep it. I took a humongous pair of pliers and squeezed the rim together as hard as I dared along the inch or two that was flared. It seemed to be a little less abrupt afterwards. A gradual flare doesn't seem to be a problem for braking, just this sudden bump. Sanded it a little afterwards to remove the burrs from the pliers, and adjusted the brake pads to catch a little lower down on the rim, since I assume the flat spot (nice term!) is most noticeable near the edge, and least pronounced towards the centre of the wheel.
I won't get to test it until I brake hard at speed, but I think I've done what I could 
And I'm going to the lbs to pick up some new brakes for the rear tomorrow. I've put it off for ages, but they're not getting any better and are not reparable.
Winter riding is much less about badassery and much more about bundle-uppery. - malkin
1995 Kona Cinder Cone commuterFrankenbike/Selle Italia SLR Lady Gel Flow
2008 white Nakamura Summit Custom mtb/Terry Falcon X
2000 Schwinn Fastback Comp road bike/Specialized Jett