One rein may cause the bit to rise on that side but will not produce the pressure at the poll.
Riding in a gag bit with two reins, one attached to the gag cheekpieces and one attached to the bit is fine; a good idea, even. You use the gag rein like a curb rein and only engage the gag when you need it.
Not sure what face and sound you're referring too; someone must really have been abusing the bit for that to happen.
I actually prefer an elevator or three ring bit, ridden with two reins. You get the pressure at the poll effect without the bit rising in the horse's mouth.