Use "noise gate" to paste room tone?

[steve]

However, the noise gate causes the removed sections to sound “dead”

That is to be expected - total silence does not sound natural.

I’m sure there’s a better way to go about this.

There’s a pair of plug-ins here that make it quicker and easier to copy and paste room tone:

Punch Copy/Paste

A pair of plug-ins for simplifying “punch in” editing. Unlike the standard paste function in Audacity, the “punch” paste replaces the selected audio with just the right amount of pasted audio to match the duration of audio being replaced, thus the speed and timing of the track is not changed by pasting. These plug-ins were developed from a feature request on the forum (https://forum.audacityteam.org/t/alternate-equal-length-paste-command-resolved/28836/1) to streamline the work flow of replaci…

If you find that you need to fix hundreds or thousands of lip-smack sounds, then you either need to improve your reading voice, or find someone else to be the voice talent.