If you are using the correct expressions there is no reason to SSB signal be the same as DSB. Try to use a quadrature signal in local oscilators in order to get the correct results to SSB.
AM is a DSB with carrier power, if you got the correct result with DSB you just need to put the carrierpower component in the modulator signal you used to DSB simulation. Varying the value of the carrier you will simulate the modulation index.