To give an example answer to my own question, the classic asset class of real estate, a.k.a. buy a house, is actually a pretty good idea under many of these scenarios. If money loses value, you still have shelter and a place to keep your stuff safe!
I think the different categories of possible future imply different strategies, which in turn has implications for what you should do.
In the case of a singularity type event, the most important element is that you live to see it. By definition it's hard or impossible to predict what the world will be like afterwards, which reduces the value of e.g. having lots of wealth going into a singularity. However it increases the expected value of living until then. Similar arguments apply to a post-scarcity world.
In the case of a disaster, the value some holdings may decline even to zero (e.g. if there are no more stock markets, equity holdings are pretty useless). In that case, physical possessions that either hold wealth or are directly useful (e.g. shelter, food, guns, medical supplies) radically increase in value.
Note that those kinds of things may also help you live longer! Prepping for a medium or large disaster is like buying insurance. Probably you won't need it, and it's negative expected value in dollars, but can be plus expected value in utility.
Finally, investments in your physical health help in all situations. You'll live longer to reach the glorious future if one awaits, and you'll be better off in many downside scenarios.
TL;DR: buy canned food, learn to fire a gun, and hire a personal trainer.
Cryonics becomes a better investment because your getting revived is highly correlated with how good the future is. The run up to a singularity will cause real interest rates to increase as investment opportunities grow. An actual singularity might cause money to lose all its value.
counter: cryonics is a much worse investment, because it requires BOTH technological advances AND societal/financial stability. It's a waste if you don't get revived, and that can happen by any failure of the company or the support infrastructure at any point in the path to it becoming cheap enough to revive you that someone actually does it.
It may still be worth it, but even if so, it's not a scalable investment - there's no way to put incrementally more of your capital into it in order to increase your future returns.
I think if you look up antifragile investment you find a lot of discussion of exactly this problem. As far as I understand, the idea is that most investments have limited downsides (at most, you lose what you put in) but may have limitless upsides in low-probability scenarios. Then you can make many small investments of this kind, so that when ones pays off, it's more than enough to pay you back from the loss of the rest. Taking your example of the nuclear bunker, if you could build one with 1% of your wealth or less, in this frame of mind probably you should. Or less dramatically, invest a bit into any technology that could reach world-changing level even if it looks unlikely, plus buy a house as well as a cabin far away from any city. Learn a little bit of skills that could be useless or incredibly useful, depending on the future.
The answers you are suggesting are more related to safe/robust investment (I'm uncertain on the correct term), i.e. investment which should be useful whatever happens, but has a capped upside. Both maintain good health and buy a house count in this category. I'm not more qualified to give specific advice here than anyone else, but if you ask yourself "what would a standard prudent person do" you're basically there.
Robust investment is what most people do in practice, and it's probably a good thing because I think antifragile investment is too easy to screw up. But under some assumption on the nature of the high variance, which I think match the kind of future scenarios that you listed, well-thought antifragile strategies could be much better. At the very least, you can copy the idea of not putting all eggs in one basket, even if you don't go all the way to make many small gambles in the expectation that at least one will pay off.
The main change I've made (which depends some on thinking that you can see at least some of the variance coming) is to keep more of my wealth as dollars in a brokerage account where I can buy options. [This does assume that, say, you would have known to sell puts in the first half of Feb 2020.]
I don't know why you'd be worried about having wasted your money on a nuclear bunker if the singularity or a post-scarcity world arrives, but here are my answers.
Do the important things for your health. DNA and allergy assessments should be less than 1k USD total, but they're very useful for all your scenarios.
After that, your second best investment will be in your social connections. Any way you can spend money to facilitate the gain of quantity and quality of your friends and family is very likely to pay off in your scenarios. This might include raising your social status through conspicuous consumption, paying off the medical debts of a friend, or sending your kid to college. There's nothing quite as powerful as having an advocate. Might seem like a cop-out answer, but it is effective.
Buy the maximum recommended disaster rations, and then put the rest of your money into a tech stock ETF.
ideas that are useful in some of these scenarios (e.g. build a nuclear bunker) they're totally wasted in the other scenarios.
That kind of goes with the territory of "high variance". If there were a simple passive investment that would be valuable in the vast majority of futures, we'd call it "low variance".
First, even if it's not as large a proportion as would be predicted in past decades/centuries, put a fair bit of weight on "regular disruption, not singularity". There's a good chance that for the next 10-30 years people will still want similar things as they do now, and will work and pay for them in similar ways. Things will shift, but not radically. This implies that a majority of investment should be "standard". DURING that time, you should re-evaluate on an annual or so basis, as horizons and predictions will shift. Still, "standard mutual fund investing, with a bit of more speculative (crypto) thrown in if you enjoy it" is a great default for things where you don't have a better idea in the next 1-3 years.
The more interesting categories are active, rather than passive. You note that improving your capabilities is more time and personal-energy constrained, but be open to opportunities where investment can accelerate it. Taking classes, buying equipment, etc. are often well worth it (and often wastes - you still need to evaluate the likely ROI).
Another active option is founding and running a business. In many areas, if you're reasonably smart and able-bodied, you can do well with a fairly small seed by flipping houses (buy, do minor repairs and improvements, sell) or by renting them for a semi-passive income stream (I say semi-passive, because it's tricky to make a profit unless you can do a lot of the management and maintenance work yourself or have an established network of people to hire). Consulting or independent software likewise is pretty demanding and iffy, but can scale to a pretty flexible (that is, appropriate in many futures) investment.
[ obDisclaimer: I am not qualified to, and I am not in fact giving investment, legal, or business advice. ]
I have considered running a business, and various other ways to make more money, but actually have moved away from making money towards trying really hard to do what I can to make the future more likely to go better. A good-outcome singularity floats all boats!
So anyone who thinks they have even remotely the sort of competence which could help build aligned AI should work on that, even if they think they aren't of the highest caliber or not seeing immediate positive benefits accruing from their initial attempts. I'm definitely of the opinion that the more people we can get working on it the better (provided that you don't hinder the best thinkers with the fumbling of the worst).
I largely follow standard financial advice, for example I have a moderate fraction of my wealth in retirement accounts. But I also put substantial weight on the future being... extremely high variance, such that I think there's a pretty good chance that "putting money away" will end up having been useless or at least not very useful. Generally I think it would be a pretty bad idea to have a specific belief about how the future is going to be extremely different and therefore wildly go against currently accepted financial best practices. But it seems highly reasonable, if one believes in the most important century hypothesis, to somehow change your investment plans for that. Here are some relevant futures I can imagine;
One problem I'm having is that while it's easy to come up with ideas that are useful in some of these scenarios (e.g. build a nuclear bunker) they're totally wasted in the other scenarios. It feels like there should be some way to convert current money into a non-abstract asset that would be always useful, and also fungible in the future. Like can I... somehow buy and store a ton of joules? Or can I somehow... buy 10 years worth of non-perishable food, to make sure I don't starve? When I try to think through these, the logistics seem to be more costly than any expected benefit.
The category that feels most promising to me is something like, invest in making myself a person more able to handle those high-variance scenarios. Gain skills in operations, negotiation, maintain good health, etc. But like, "become a stronger person" is just the kind of thing I'm always trying to do anyway, and it mostly seems to require time and cognitive resources. The thing I'm trying to figure out is how to convert money into being a stronger person.