ZJX FLM reported traffic for a sector being over the Monitor Alert Parameter for the sector.

Narrative

I came into work at XA:45L and after I did my weather and CEDAR I needed to Track for X sector; Y sector. The sector had a D side; 2 Trackers; me included; and the Radar controller. The weather was a massive extreme precipitation on the scope coming in from the west and it was causing all aircraft at all altitudes to deviate towards sector X. The NAS monitor at one point had a red 50 number. Within minutes of plugging in I shut off all south bound traffic coming from the north to help the sector and we also shut off all departures to be able to recover. The amount of aircraft in the sector was unmanageable; exceeded capabilities of the sector; and was the worst session that I have ever seen in X years of being a Supervisor in the Area. I am also Radar certified on X [sector] and it was extremely unsafe situation. Recommendation - Need route structure when weather impacts happen. Shut off departures sooner. Hold or shut off south/north bound sectors to help slow traffic. Need a slower traffic rate when other sectors get shut off from weather.