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Use Cumaru hardwood (aka Brazilian Teak or Golden Teak). My internet searching seems to indicate that this wood has a Class A fire rating and is as resistant as concrete to fire.
This link includes a number of results from test data backing this up.
The type of testing that these hardwood decking and siding species were tested for is commonly referred to as ASTM E84-10 "Standard Method of Test for Surface Burning Characteristics of Building Materials". This fire testing standard was established by ASTM International (formerly known as American Society of Testing and Materials). A Class A fire rating using the ASTM test method is the equivalent of a Class A fire rating from the following test methods and agencies:
- ANSI/NFPA No 255 from the American National Standards Institute/National Fire Protection Association
- IBC 8.1 from the International Building Code
- UL 723 from Underwriters Laboratories
In short wood is not the right material for this, I think you should re-think the requirements... coming to the inevitable conclusion that metal is very likely the way to go. Every fire-pit cover I can recall seeing was made from plate steel.
But if I'm reading the following right you already have problems you'll need to address!
a firepit made out of wood.
There's a reason barbecues and so forth are made from metal, brick or concrete, just sayin' ;-)