Here's my proposal: Implement the new PoW as a PoWA (proof-of-work additions) soft fork. New PoW is memory-hard Cuckoo Cycle (whose creator has joined the discussion here), or possibly Equihash.

Give 5% of the block reward to the new PoW. This is enough to create a new DRAM-based mining community + hardware/software infrastructure without alienating/bankrupting existing SHA2 miners.

If SHA2 miners continue misbehaving (blocking Segwit, threatening to use other implementations), we increase the new PoW's reward with another soft fork. Hopefully this option won't have to be used: the threat will be enough to keep them compliant.

Conservative approach allows us to use relatively untested PoW algorithm safely, as blockchain continues to be 95% secured by old SHA2 hashing power. Getting the larger community behind a conservative solution will also be easier. Pro-Core miners will support it, since it's a far better option for them than the current standoff and possible network fork.

This may be the best way to get a POW change started as it gets everyone used to the idea. If things go south quickly, I'm sure the transition could be accelerated through another SF (more palatable at that point) or even an emergency HF.

Couldn't this be implemented as a UASF instead? The SHA256 side can be rendered insignificant from the get-go and blocks would still be backwards compatible.

I think a hardfork change is too drastic, and will certainly end in a contentious hard fork.  A POW change light can be implemented as a soft fork by a requirement for an extra proof of work of a different type in the coinbase transaction or in another special transaction.  This will encourage cooperation between miners having lots of specialized SHA256 hardware and users mining the extra proof of work on their CPUs.  If miners behave badly, users will turn their backs to them, and it will become more difficult/expensive for the miners to create new blocks.  Another important advantage is that old nodes and wallets will still work, as long as the majority of the hashrate is behind the soft fork.  Still safeguards must be put in place to stop someone with a very large SHA256 hashrate to overtake the main chain at a later time when the extra POW difficulty is high, since a SHA256 only chain will still be valid for old nodes and SPV nodes.

I found that the HF future contract of Bitfinex is very unfair against big blocker. 2 support BU supporter, HF should be accelerated.

You do realise that the PBOC prints electronic fiat at zero cost?

Why would it be too late after an attack to HF? A few txs get stolen or blocked?

By my estimates 95% won't preemptively fork the PoW algo ... do you really think you can convince them all to preemptively HF?

I am being pragmatic

Bitmain could pre-emptively fork themselves during an unknown 24 hour timeframe, with 75% of the hashrate and a pathological desire to destroy Bitcoin, why do they need to even pretend to be cautious?

We should assume the worse and prepare for it , I just don't agree with you practically that doing so preemptively will lead to better security , in fact I believe it will lead to far less security because few will follow such a HF

Ok, now please provide a formal proof for minority of readers who can't understand an informal one (e.g. me).