Hmm. This is cool.... let me check if I understand it correctly. Also, this might help others understand in more laymens terms (if I got it right)

The ProblemThe Problem

You have coins sitting in a quantum-vulnerable address $A$, and you failed to move into a quantum-secure address before Q-day

The SolutionThe Solution

A soft fork that still allows people to spend from quantum-vulnerable addresses, but only with additional proof of ownership. The protocol relies on the existence of "knowledge asymmetries"... information that is hard for a quantum attacker to crack, but the true owner of the coins would have. We'll assume that such a knowledge asymmetry exists, and we'll call that secret $S$, which proves that you own $A$.

How it worksHow it works

1. First, you create a new post-quantum keypair, $(Q,q)$. ($Q$ is the public key, $q$ is the private key).
2. You use $Q$ and $S$ to broadcast a "timestamp" transaction on block $T$. The purpose of this transaction is to prove that you knew $S$ at time $T$. $S$ and $Q$ can't be reversed from the transaction data.
3. After a delay of $d$ blocks, you publish a "rescue" transaction to move the funds from vulnerable address $A$ to post-quantum address $A^{\prime }$. The "rescue transaction" reveals $S$, thus proving that you control $A$, and it also contains proof that you published the previous timestamp transaction.

Reason for the timestamp and the delayReason for the timestamp and the delay

4. Once you send your rescue transaction to the mempool, $S$ is revealed. Without the timestamp/delay scheme, anyone can take that information and race you to moving the funds from $A$. However, because the protocol requires the proof of timestamp, the attacker would first have to create their own timestamp. But since you didn't reveal it until time $T+d$, they'd have to wait until at least $T+2d$ to steal your funds, because they'd first have to create a timestamp at time $T+d$ (when they see $S$), then wait another $d$ blocks.

Advantages of the approachAdvantages of the approach

Allows people who failed to migrate to post-quantum addresses a chance to recover their funds, while at the same time not letting vulnerable coins become exposed to a quantum free-for-all.

Does that about catch it?

I think your article has a lot more details about miner incentives and other implementation details, but I just tried to capture the high level gist of the idea.

Thanks for explaining commit/reveal. It's a powerful scheme.

Generic comment, not personal (I know that this is what you meant with "controversial" and that you acknowledge this in your bottom "drawbacks" item.):

Any wallet created with Bitcoin Core version < 0.13.0 (2016) will have a random() sourced keypool. Can still be p2pkh, single use, and secure against everything but in-mempool / reorg-driven replacement by a quantum attacker. Any proposal that asks for additional proof post Q-day, no matter which flavor, will always confiscate every coin in such a wallet.

What is needed to make people come to their senses and not propose confiscation, ever? If there is insufficient disincentive to proposing it, then maybe this disincentive must be created, but it would be much better to for once not walk the same path of toxicity and just collaborate to enable decision making, rather than making them for people as if Bitcoin is a nanny state.