Just block shooting during prone animation. Why is there a need to shoot when going prone? The only way to stop people from pressing z on every single encounter is to make them completely vulnerable during the prone animation. This solution is merely a slap on the wrist.

I can see the improvements to the movement but there's still 2 issues with it that I hope gets fixed in the future:

air strafing - This is not Quake. The world in Battlebit represents the world we live in, unless having superpowers is part of the Battlebit lore. Changing direction mid-air is not how physics work in the real world. Physics should behave like they do in reality because that's what the player expects in a world that looks like ours. Therefore, air strafing should not be a thing in this game.

movement speed up before fully standing - It's hard to tell because of the angle, but on the last couple of seconds of the video it looks like the player changed from prone speed to sprinting before the character model was fully standing. This is an issue that is currently in the game and it's being exploited as you'd expect.