Definately check trans mount , both L &R steering rack mounts (these need to be SOLID- not "beaten"), anything utilizing rubber as a "base mounting". Lesser extent sway - bar, link ends,etc. etc,even a sub frame rubber spacer may have disintegrated ?? Most of this rubber is not too bad of a job. Just shake in all directions vigorously to size up their integrity - can be loose in one plane only , you know.
Many may look fine but have unseen damage OR taken on the the consistency of a Gummy Bear compared to "New". Some replacement crap float'n out o' the bay use that cheezy soft rubber , conversely some utilize very hard inferior rubber - both bad! Beware'
My J30 @ 260kmi , some shimmy was corrected by replacing just the passenger side rack bushing , L side seemed OK , I stopped there , and that virtually eliminated ALL the noticeable shakes.Left side part was
scarce O/S , twice $$ of RT bushing , and VERY harder I believe to R&R
Tip : IF running higher tire pressure , like 36+ psi HOT, FIRST try dropping a full 5 or 6+ psi for $Hi%%TS & grins.For effect , see any improvement ? - ya take it from there. (Flat-spotting???)