Voltage does not affect the torque constant.
If you're limiting the motor current to 300 amps, and assuming the lower voltage does put out 300 amps at the start, you won't notice a difference in torque at the start. However, a higher voltage will increase the range of speeds which the motor current will be limited, so the torque will remain higher at a higher voltage after you get past the speed which the motor current starts to drop for the lower voltage.
So, in essence, you'll get more torque with a higher voltage somewhere in the middle of your speed and past that speed (The speed at which the motor current starts dropping for the lower voltage), but you'll get no difference in starting torque.
If you're limiting battery current to 300 amps, the higher voltage will have a higher torque since the motor current and, thus, torque will be greater.