Not meaning to criticize, but I really couldn't understand more than superficially what you described as, "...sort of a ka-thuck-ka-thuck motion...." No offense meant.
But, re "...steering wheel shimmies side to side while the car is moving....", you write that the effect correlates to the speed of the car.
So, aside from the possibility that this is still related to the bad rotors, consider two other possibilities:
1) a bad wheel bearing.
2) a tire tread separation.
Each of these can give a pronounced thumping feel on the steering wheel, and of course this will sync to the speed of the effected front wheel's rotation.
The distinction between these two possibilities is a subtle sound, and it's not uncommon to confuse the two.
1) Considering tread separation, jack up each front wheel only slightly, so that the car's weight is off the tire and the tire is only barely off the ground, only enough so that you can spin the tire by hand. If there's a blister on the tread, its bulge will block the free motion of the tire at one point -- the tire will freely spin over the rest of its circumference.
2) Considering a bad bearing (if you didn't find a blister on either tire by step 1), then jack each tire completely off the ground and give the tire a really strong spin. You might hear the bad bearing by it's metallic rubbing sound. Trouble is, sometimes it only occurs under the load of the weight of the car :-( , but it's worth the try to diagnose it this easy way.
And, of course, also tug on each tire at 12:00, 3:00, 6:00 and 9:00 positions to feel if there's any slop or excessive free play, another sign of a bad bearing.
Good luck.
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