I tend to use Waves RVox Compressor/Gate. The downward expander is not a conventional "on/off" gate. It provides a gentle reduction of the noise floor by means of a soft knee behaviour. You set it by ear and instead of sections of sudden absolute silence, which can be very noticeable, the unwanted noise is reduced but still there while, if necessary, the overall level increased by the compressor. Worth a try if you have it.