Nissan 300ZX engine rocking problem

My 300zx starts and runs fine but for the first few minutes it sounds like something is off forcing the car to shake back and forth (sometimes violently). It doesn't matter if it's a cold or hot day. It does this for a few minutes and then it runs smooth afterward no matter how long I drive. This problem seems to be more pronounced when the gas tank is 1/4 or less full but it's much better when the tank is full. I have given it a good tune up including changing the spark plugs, distributor cap & wires, the fuel filter, etc. I don't know if the fuel pump works harder when the tank is close to empty because it's damaged or maybe the timing needs to be adjusted or what? I'm puzzled. Any advice?