There's a twist to this profitability statistic, which I haven't seen mentioned anywhere yet: your reward for mining a block can be spent only after many other blocks are mined on top of your block.

That changes the game significantly. What matters for a miner is not "it's more profitable with the current difficulty and price", but instead "it's more profitable with the current difficulty and the price X blocks in the future". Moreover, once they've mined a block on one chain, it's in their interest to keep that chain alive and working well for at least X blocks, so they can convert enough of their reward into fiat to pay their costs. The obvious way to do it would be to keep mining on the same chain, which generates yet more block rewards to be claimed later. All that might make the chain choice somewhat sticky for the miner: once on one chain, it's better to keep on the same chain instead of switching every time the price swings.