As to 571.107.1.(7), there is no conflict with 571.030.1.(5) because 571.107.1.(7) does not specify any kind of prohibition or restriction on possession of a firearm while intoxicated, it simply points out that nothing in the provision specifically authorizes such an action.
As it stands right now, it is perfectly legal to be falling down drunk and in possession of a firearm in Missouri (provided that you are otherwise lawfully entitled to possess said firearm).