I believe Fernando is on to something here, though. Despite this functionality being in an add-on that is currently stable, I feel like natively NVDA can include a change based on his suggestion. After all, add-ons are created because of a desire by users, and I feel this is longed after by many, including myself. The fact that screen curtain, focus highlight and Windows 10 app support and changes were once add-ons, and are now part of the core of NVDA, says a lot about the possibilities they possess.
Now, I can see this working similarly to the current screen curtain implementation. When the gesture is pressed once, NVDA speech can be toggled to off. If pressed twice quickly, however, NVDA speech can be set to beeps. To turn back on NVDA's speech, just press the gesture once when it is either set to beeps or off.
I honestly think this would be even better than what we have now, as sometimes cycling to the different speech modes can be confusing, especially for someone who may want beeps and is a new NVDA user.