Here is the best order of operation of things to check.

1: correct wheel hub size-if bad hubcentric rings
2: steering rack bushings- if bad FIGS steering rack bushing
3:wheel balance- High speed balance
4: outer tie rod ends-replace
5: inner rods-replace
6: wheel hub- can normally tell by a humming or ticking on turning under load.
7:Steering pre-tension adjustment- I recommend this just for more personal steering feel.

 

Talking my friend at Lexus he said inner tie rods on the GS rarely fail. I can say from experience on my Buick, that when struts in front are bad, inner tie rods take a bad hit and life is short on them. They get moved a lot more than they should (up and down).

As low cost are they are and how easy to replace, just do them if you are in doing inner tie rods anyway.

On my GS (following EITELS123's list)

I have Factory wheels, (no issues)
Replace rack bushings (mine were pretty bad)
Wheel/tires Road Force Balanced
Inner and Outer tie rods replace (ok, right inner still stock, but still ok)
No noise on bearings.
Leaving steering pre-tension alone on mine, it might be too tight if anything....

Any shake I have had has been brake pad material deposited the rotors. Clean it and shake I had was completely gone immediately. Some call it warped rotors, but reality is that is super RARE. Clean them with a sanding disk or a razor blade. It is the inside that is most commonly a problem.

OP, note what brake TEMPERATURE is worse, cold or hot for shake? Mine was bad cold but after the brakes warmed up got better. But one day last year it suddenly got REAL bad. Was a bad caliper. Fixed and cleaned rotors, 100% perfect after that.