The problem with the SoftwareSerial and the standard servo library is that they both use the same hardware Timer.
No, SoftwareSerial does not use a timer. But it's programmed so badly that it blocks the complete CPU during send out and reception of complete bytes. As the timer interrupts are not handled during this time, the signaling for the servos get out of sync.
You might get it to work if you let the hardware PWM do all the servos stuff and use one of the interrupt serial emulations but the best solution is definitely as -dev suggested: use the hardware serial interface. If you need more than one serial interface, change the hardware platform (Leonardo has one additional hardware serial, Mega2560 has 3 additional hardware serial interfaces).