Could be OD drum is out of round, but wouldn't explain why it shakes at idle.
Not a Ranger issue, just general automotive issue, nothing sticks out as a 1999 Ranger 3.0l or a 4R44E trans issue.
EGR valve is not used when engine is cold, so if you still have shimmy when engine is cold then won't be EGR system.
After engine is warmed up you could remove the vacuum hose on the EGR valve, and then plug that hose with a bolt or screw.
Drive truck and see if shimmy is gone, CEL(check engine light) will come on after a bit, because EGR is unplugged, it will go back off after a bit when it is plugged back in.