It could be any number of things. Usually to check for warpage, you'd use a dial indicator that is anchored to a stationary surface such as a stand on the floor, but I understand that this is not a cheap/common tool to come by. That would give you the most accurate indication of whether the rotors are warped.
A wheel bearing could be worn out, causing the whole hub to move when the brakes are grabbing really hard. The only problem with that theory is that the bearing would be noisy while driving.
It also could be the ABS activating prematurely. If it is easy on this vehicle, I would remove the wheels and pull out the ABS sensors. Clean the tip of the ABS sensor as well as the pulse wheel attached to the hub. If metallic brake dust is really caked on both of those components, it could cause the ABS to act erratically.
Another problem could be warped brake drums in the rear, since the rear brakes aren't really activated until you press the brake pedal very hard. I'd say getting them turned would be a last resort - it would be easiest to clean up the ABS sensors/pulse wheels first and then go from there.