That hump that flares out would easily produce the sort of pulsation you're feeling. Often such a thing occurs at the joint of the rim if the weld wasn't dressed correctly.

If this were me and I wanted to save the rim and if the rest of the rim was quite consistent I'd mark off the extent of the flare's edges and peak on the inner spoke arc of the rim so it can't be scuffed away and then I'd carefully work down the excess metal with a fine cut file. I'd also use a good straight edge to see if the flare is all on one side or if it's even on both sides. All of this fine measuring would determine how I proceeded with dressing away the excess metal.