If rebalancing of the tires doesn't cure the problem, I have another suggestion to bring up. If you rotated the tires front to back, after not having rotated them for quite a while (say 20,000 miles or more), then it could be caused by the former rear tires now in the front. Tires left on the rear too long can develop cupping from all the bouncing they are subjected to on the rear of the car. Since Camrys are front wheel drive cars with something like a 65% to 35% front to back weight distribution, (like most front wheel drive cars), the rear tires don't carry that much weight. As a result, they bounce quite a bit while driving. This constant bouncing without proper rotation can result in cupping of the rear tires. You don't generally feel the problem while the tires are still on the rear of the car. Move those tires to the front and you feel the problem created by the cupping. To varify this problem you can try rotating the tires yourself front to back and then taking the car for a ride. If the problem goes away, you have isolated the problem to the cupping of the former rear tires, now once again in the rear. Your only alternative is to get 2 new tires and put them in the front with the old front tires once again being rotated to the rear. Then I would suggest rotating your tires at least every 7500 miles.
Mike