Flame retardant plywood or other code-friendly ceiling material?

Greetings all!
My wife and I purchased a partly completed house in Southern California, USA, about 6 years ago, and with the help of a contractor friend, finished it. It passed inspection, and we have lived relatively happily since that time.
The structure has three levels -- a 'basement' at ground level, and we only call this a 'basement' since about 1/3 of this floor is about 4 ft. below grade. There is also a completely finished main floor and large loft.
The 'basement' was mostly finished by the time the County signed off on us, but a large room (maybe 400 sq feet?) was left unfinished. We now want to finish that space as a billiard room with Tiki Lounge stylistic elements. The major thrust of this effort is as follows:
(1) The space is an awkward trapezoidal shape (long story) so we plan to partition off both the north and south ends of this space for storage and utility areas. This means two partition walls. Not too worried about this part.
(2) Some lighting fixtures and plugs will need to be put in. Having a professional do this, thus am not too worried about this.
(3) The ceiling is currently just the unfinished joists of the floor above, and finishing this bit is what is causing us grief. Due to some very, VERY, complicated angles, a hung ceiling seems like a nightmare. Given the weight of large panels of drywall, we also aren't too keen to try to drywall the ceiling. We'd like to affix some kind of plywood (or other easy-to-use material) onto the joists and then staple lauhala matting (from the delightful pandanus palm) onto the ceiling. The problem here is one of fire.
Are there any products that we can use as a ceiling BESIDES drywall which will satisfy most codes? Some kind of flame retardant plywood, for instance? Are there any kinds of drywall we can use that are lightweight enough to be easy to handle, and yet which also provide sufficient fire protection to satisfy code?
Turning to the matter of the matting: There does exist flame retardant matting one can purchase, but it is kind of expensive; rather than buying the expensive pre-treated matting, I'd prefer to buy the regular lauhala matting and apply a flame retarding chemical product (of which there are many) myself. Will lauhala I treat myself have approximately the same flame retardant capacity of the pre-treated lauhala? Will lauhala treated with flame retardant pass code, or is the very idea of matting on the ceiling (even if treated with flame retardant) forbidden nowadays?
Thanks for any advice concerning any aspect of this bundle of issues. I certainly do not want to do anything that puts me at risk for fire or which puts me in violation of code.
P.S.: Some of this code business seems a bit absurd sometimes, but perhaps it is just because I am a layman and do-it-yourselfer...maybe if I were a pro it would make better sense. But here's one thing that strikes me as odd: We passed inspection with this roomful of exposed joists in the basement, and it seems like WHATEVER we do to finish that room will decrease our fire risk. So naked joists are fine, but I bet if I nailed plywood to them, I would be in violation of some code. Oh well.

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