Have you already stuffed the joist-bays with insulation? If not, You should investigate Homasote and similar compound building panels that combine insulation and fire-resistant surfaces in one panel. (Which would go across the joists, instead of between them.)
If you *HAVE* put the insulation in already, then sheetrock/plaster board really is your best bet. It's not as hard to work with as you apparently think it is, especially if you cut it into manageable sizes before moving it.
If you have a neurosis about the rock panels, then you could use something like Sunforger Marine Canvas (Which is available in the US in 100-yard rolls from ITEX/BANWEAR) It's fire and mildew-resistant, which doesn't mean it won't mold and burn, just that it's not quite as eager to do so as regular canvas. I suspect it's some sort of boric acid treatment. The canvas won't meet code, but it's better than either exposed insulation or stapling up old refridgerator boxes.
If you're cheap, and don't care about either meeting code or burning yourself to death, use white muslin, after giving it your own boric-acid/borac bath in your tub. or using a commercial fire-retardant on it.
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