This is to answer the question: "What mechanism prevents a large BTC mining pool from switching chains and 51% attacking BCH?"

First, who are miners? Many miners grew their operations when Bitcoin was still one, when it was supposed to become a peer-to-peer electronic cash system. Therefore, I think it is safe to assume that many miners have hopes for BCH.

Hashpower distribution doesn't reveal any miner's ideology, political position, or preferred SHA-256 blockchain. This is because it's a competitive market and they're forced to mine according to a simple economic calculation. If some big BTC pool can "attack" BCH, then another big BTC pool can "defend" BCH. Problem for the attacker is: he has no idea how many other miners would step in to defend. Because of that, the cost of the attack and its chances of success are unknowable so there's a natural deterrent. This is a consequence of sharing the mining algorithm. It'd be easier to attack a blockchain that has some novel algo, as there'd be nobody out there who could step in and overpower the attacker.

Miners mine what pays, and their total reward comes from combined value of ALL SHA-256 block rewards. During normal times, it's rational to allocate their hashpower proportional to USD value of SHA-256 block rewards, adjusted for difficulty. Deviating from that wouldn't necessarily mean a direct loss, but it'd mean they'd be earning less than they could be earning, what is known as "opportunity cost". Because total reward comes from ALL SHA-256 coins, it is in the interest of SHA-256 miners that ALL SHA-256 coins survive.

BCH making it to $50k alongside BTC at $50k would be great news for miners regardless of their ideologies, because their total reward would double! They shouldn't care about relative BCH/BTC ratio, what matters is that they both appreciate against whatever we use to price energy.