Re-do your analogy but now it's that your dad killed someone and stole the deed to his land, found oil on it, and is now one of the richest people in the world and the person he killed's kid is now on the street begging for cash and tell me again how little you owe that kid who's father's land gave you your trust fund and your college education.
That's actually not that hard to do, both from a legal and a moral standpoint. Legally, the "you" in your analogy has never committed an unlawful act and is therefore not personally beholden to any restitution to the victim's side. It is the purveyance of a well-functioning justice system to provide adequate restitution for victims of crimes, but that does not extend to a personal obligation on people that had no part in said crime.
Morally, the story is a bit more convoluted but your premise falls back to the theory of original sin: that people can be personally held responsible for their heritage. In the past two-thousand years it has been proven a very powerful argument because it "feels" right, but at its core it is still a rejection of the individualist premise that all people are born equal. And I'm still on the side that believes all people should be born equal, even though that stance seems less and less prevalent nowadays. Once you start arguing for collective punishment of past crimes, it's very hard to argue your case without at the same time defending the same practice throughout many wars in history, and now explicitly outlawed in the Geneva Conventions.
In fact, the concept of original sin requires that we exist in a state of punishment for that sin permanently, not that we continue to benefit from it by, again, existing in the wealthiest civilization that has ever existed on this planet.
This is again a poor analogy, framing us as victims of an aggressor who wants something from us that we cannot give.
As for the geneva conventions, please note that colonial relations to indigenous people violated just about every single one of the geneva conventions. Forced resettlement, biological warfare, collective punishment, the destruction of non-military targets -- it is not "collective punishment" to expect there to be at least a moderate reparation for crimes committed. What is even the point of the concept of "war crimes" if you can get away with them just because "oh it's been too long".
A better analogy would be: your grandparent barged in to a persons house at gun point, demanded him to hand over his house. The owner obviously resist, and your grandpa tells the original owner that he will be given his house back in a couple of years(legally signed) to ease the resistance. This paper was also signed "with the current owner of the house", in mind(in case grandpa dies).
Now the original owner lives on the street, his grandchilden the same. Each generation have always asked "when would you live up to your promise?" to the descendant of your grandpa (current owner of the house) each year.
Now you can of course discuss if you should give additional compensation for their suffering, but the original contract still stands, and you've always been obliged to follow it. It's not about blame.
disclaimer: I'm in general in agreement with you that I don't think a child should be blamed for their ancestors sins.
This is a fundamentally flawed analogy. Our government - the same government that has existed since these treaties were signed - is still around.
> I find it very difficult to find the moral obligation to pay back that money when the people who were the actual victims are long dead
The question of a "moral obligation" is entirely irrelevant and unrelated to our government's legal obligation to uphold the treaty that our government signed.
I think you are making this too much about personal blame, and sin, and ego. Your analogy falls apart right out of the gate because the premise is off. It's not about placing blame or making you feel bad.
As long as restitution has not happened and you are still profiting from the act of wrongdoing and the victim (or their descendants) are still suffering from it. It's pretty simple, isn't it.
The facts are that the colonists / invaders genocided and displaced the original inhabitants of a continent and moved the survivors into reservations, probably to avoid it going down history as racially motivated genocide entirely.
Sure, you didn't do it, your ancestors probably didn't have anything to with it (or the slave trade for that matter), but that doesn't mean you shouldn't fight for other people's rights. They still suffer under what happened a hundred-and-then-some years ago, they are a people whose country was taken from them, whose culture was (attempted to be) erased, and who today what little they got as a consolation has also been attempted to be taken from them because said consolation actually did have some value.
Your analogy is wrong, oversimplified and trivializing the issue.