Forcing people to be responsible for more than their immediate actions

What you're saying is that children should carry the responsibility for the acts of their ancestors.

if I include an unjust status quo in my reasoning, then I might also use violence to free myself from the consequences of past violence, but that would not create a “cycle” wherein a stable, nonviolent state cannot be reached, since every “allowed” instance of violence would still only be associated one-to-one with an equivalent instance of “disallowed” violence.

Who's the judge of whether it's "allowed" violence? If we say that the status quo of Franco-German relationship is built on the past injustice, and that this should be fixed, who will count all the past centuries of wars and massacres and calculate the outstanding balance?

Because if you let it both sides do it for themselves, then they both will naturally come to the conclusion that they've been unjustly treated and that the other side has to pay for that. In the end it will be the stronger one, not the morally correct one, who wins. For a time, then the sides will switch => cycle of violence is IMHO unavoidable if you hold the opinion that past sins are never forgotten.

Now, if my family’s wealth was robbed long ago, I would have a right to recover it

History is basically never so nicely clear-cut. I mean, have you studied your family tree and made sure that all of that family wealth was gathered via perfectly moral means? What if it turns out that your grand grandfather was a soldier who brought home some gold of dubious origins?