Hmmm definitely a bent chassis
j/k These issues suck! I think the mechanic would notice worn tie rods but that's a possibility. Tire balance & alignment never hurts.
For sh*ts and giggles try toggling your DTC to see if that changes the characteristics of the shake. I'm always suspicious of the computers behind our steering when stuff goes psycho like this. There might be a way to reset the whole steering system. If you have time, call the dealer and check if it's possible... I've had bump steer & tracking issues that resolved after a limp mode.