I'm not familiar with the script, but try this code in a Script call:
$game_system.hud = false
And to turn it back on:
$game_system.hud = true
From what I could tell, however, the player would still be able to turn the HUD on and off by pressing the button which controls it. If you also want to prevent the player from bringing it up, you can use the following code:
$game_system.hud_button = false/true
Where false would prevent the player from calling it, and true would permit the player to call it up.