This is a typical issue with static boomed mics and talent unused to working to the mic. For your type of shoot, I'd suggest a hard-wired lav - wireless isn't necessary for stationary seated subjects.
The one time I tried a noise gate when I was working TV was the last time, and I "tried" it. I didn't end up using it. Gating production dialogue is the last thing you want to do. It makes the room noise stand out even more.
