To state the obvious: if you die before you get the paperwork straightened out, it’s not your problem. And it sounds like there’s no one you really want to help from the grave. So, it’s not really your problem, now, either.
Not wanting to go too much farther down a hijack.
You’re right that dead people have no problems. But as a living person now I can feel bad now about knowingly setting up an ugly mess for somebody to clean up later.
But far more important than that:
The single most important “paperwork” one ought to have is a trust containing all their assets with somebody trustworthy named as trustee to manage your affairs when you are incapable but not dead.
I could stroke out tomorrow and live 20 more years. Absent proper pre-arrangements for that, I’d be in a world of hurt. With proper arrangements I’d still be gorked. But I’d have people who are legally empowered to take care of me and have legit access to my assets to fund that care. Absent paperwork, neither of those things are true.
Probably the same way that it used to be done in the US - my mother most likely never knew my social security number since I applied for it either when I opened my first bank account or when I got my first job and she didn’t need the number for her tax return when I was a kid.
Who will be your executor? If you have a lawyer doing it, they are being paid to do whatever it takes to execute your will. They will gladly spend $$$/hour until the estate is drained dry. But if it’s a family friend or relative doing it as a favor, do them a favor and try to make it easy as possible for them. It’s a big burden for regular people to be the executor even when all the heirs are known. They have to deal with trying to navigate unfamiliar legal territory and heirs with potentially problematic desires. Adding in trying to track down people who have cut ties will be more burden for them. However hard you think it is for you yourself to find them, it will be even more difficult for the executor. If you are just leaving them a trivial amount, perhaps reconsider that. Perhaps leave them a sentimental item that could be stored with one of the other heirs if they ever make contact again. Or at least, try to track them down now so that at least the executor has a recent data point to start from.
From a legal standpoint, could a distribution have a time limit attached to it. For instance, "I leave $$$ to Joe Smith, currently estranged, location unknown, provided he contacts the family within 1 year of my death. If he doesn’t make contact in that time, then the $$$ is to be distributed per stirpes to the remaining heirs. " That way the executor doesn’t have to burn a lot of time and money trying to track down someone who may not want to be found.
I endorse this post in all of its aspects. Probate can not only be lengthy but expensive, and that money comes out of the estate.
Can you leave a bequest in a new Testamentary Trust on behalf of a difficult to locate person? Then the will can be executed fully. Meanwhile the bequest is available if the person is ever found.
The rub is that if the person is never found, the money sits there. Not sure if there is a way to also specify a timeout, but it seems likely.
In most English-style trust law systems, you must specify a timeout: You can’t set up a trust of indefinite duration, it must come to an end - traditionally within a “life in being plus 21 years”, but the precise calculation of this clause is subject to many pitfalls, which is why many jurisdictions have replaced it with a more clearly calculable statutory period. This is called the “rule against perpetuities”, and exceptions exist (especially for charities). Under its traditional strict interpretation it doesn’t just mean that the trust is automatically put to an end upon expiry of that period but rather that the trust is void if the settlor doesn’t include clauses that ensure that the trust cannot, even theoretically, extend beyond this period.
You said two estranged children. To the best of your knowledge, are the two of them still in contact with each other?
Assigning US social security numbers at birth is actually something new. I went down to the SS office and got mine when I got my first official job.
And are they in contact with your non-estranged children?
@Chronos and @Alessan, they are neither in contact with each other, nor are they in contact with the non-estranged kids.
Well, relatively new, anyway; it started in the late 1980s, when it became law for parents to have to list the SSNs of dependents in order to declare them on their federal income taxes.
Presumably, when they inherit that money, there will be income tax due on it. So your equivalent of the IRS (Inland Revenue?) will have an incentive to assist the executor in delivering that inheritance.
In Australia windfall money that you get from a will inheritance (or a lottery win) is not taxable. If you get an income-generating inheritance, like taking over the old goldmine, you get to pay all the taxes that any owner would.
No inheritance taxes 
? Even for billionaires?
Nope, a strange nepo-anomaly in the Workers Paradise. Without starting a hijack, that whole issue of intergenerational wealth transfer is v contentious and currently a live political debate.
I assume the same as Canada. The catch being, unlike the USA, (my understanding) any assets with capital gains due will be deemed to have been sold at the time of inheritance (or if transferred to a trust) and tax due. (Exception for primary residence, exceptions for some stuff between spouses, etc.) Unlike USA, Canada wants it’s tax dollars from the well-off.
What I would do is put a time limit. If these heirs cannot be located with reasonable effort within, say, six months, those shares are divided (however you prescribe) among the other heirs.
It is good that you are thinking about this beforehand. I have a friend who has spent the last six years trying to administer his FIL’s estate because it made no provision for a complcation and the heirs have been fighting over it ever since.