I'm notin the know about the cressida's front end set up, but it is possible that the extra load from the 1G-GTE could be altering the tyre contact patch being used. This probably won't happen if it's a double a-arm, mac-pherson strut or double wishbone set-up, but if it is single A arm etc etc then maybe this is possible.
Dunno, just a thought that came to mind.
Also, out-of-balance tyres/wheel can cause pretty bad vibrations.
28psi pressure is probably a bit low, but is probably not the issue in this case.