Those symptoms could also point to a bad tire. You said they were balanced, if a belt slips or breaks it can still balance fine all while still giving you an out of balance feeling. I have had a tire go bad once and it made my car pull to a side.
Years ago I bought a set of cheap snow tires for my car at the time. I turned around and went back after I picked up the car, I thought they forgot to balance them... Turned out 3 out of 4 new tires had bad belts. That was the last time I bought Chinese rubber.
96 Cougar Sport - T45 Swapped