You could create a DeFi system not too unlike the one linked in this post: a number of oracles release keys at designated times (use M of N encryption).
The oracles could be financially incentivized to behave properly. E.g. they post a bond, which is confiscated if they don't post a private key on time or if a whistleblower discovers and reports a key early. In return for correct behavior they can earn some fees paid by users of the service.
The financial incentive still flips if the secret's value is sufficiently large, but it would require coordination of many unprincipled oracles.
The problem with whistleblowers is that now the entire system's security is transferred to them. Whistleblowers can also be bribed to blow whistles early or not blow whistles.
Here's an another idea. Bitcoin has a halving, right? Somehow the entire system has agreed to halve at a certain time, and not halve early or halve late? How does this work? Can we utilize this time agreement somehow? Can it be incorporated into an algorithmic whistleblower, whereby (a) N people each know 1/N of the key (b) if anyone demonstrates that they know the answer to a question before halving, whistles are blown by a contract and all N people are punished (c) after halving, all N people receive a reward?
Anyone can halve at any time, so anyone can "cheat" that by halving immediately.
The reason everyone does it at the same time is because doing it [literally right now] will lead to a history that nobody else agrees is valid (halved at the wrong block number), so any coins you mine on your forked chain will be worthless. There's a monetary incentive to play by the rules, but absolutely no technical requirement.
Bitcoin's primary achievement (IMO but it's fairly common) is that it managed to design a technological system that encourages playing by the rules. Cheating always pays worse than playing along, and even trolling only works if you have the majority of all computing power (very expensive), so there's no reason to cheat. But outside the core public key cryptography that handles addresses and proving transactions, and the "proof of work" that basically just limits the speed of everything so there's time for the world to agree on things, there's not really any fundamental crypto involved. Just self-reinforcing social incentives.
(this kind of disagreement is why there's both Bitcoin and Bitcoin Cash. they share a common beginning but branched off some time ago and are now completely separate)
The whistleblowers are not designated parties, they are just any Ethereum user. They would have a financial incentive for whistleblowing, and they could never falsely whistleblow because the smart contract can check whether they actually have the private key early or not.
The oracles could be financially incentivized to behave properly. E.g. they post a bond, which is confiscated if they don't post a private key on time or if a whistleblower discovers and reports a key early. In return for correct behavior they can earn some fees paid by users of the service.
The financial incentive still flips if the secret's value is sufficiently large, but it would require coordination of many unprincipled oracles.