It may not be the biblical interpretation that is wrong, why cant it be the dating of the artifacts as wrong?
Do you think that everything they date is 100% absolutely accurate? Perhaps those tools that they find may not be as old as they think they are.
Radiocarbon dating is very accurate, and it works for things up to about 50,000 years old.
As long as a person (or any living organism) is alive, they're taking in carbon from the environment - this is how we build our bodies and have a functioning metabolism. This carbon we take in isn't all one isotope: some of it is stable, but some of it is unstable forms that will break down over time. We know the rate at which these isotopes will break down based on fundamental principles of nuclear physics.
In the environment around us, these isotopes are in a particular ratio with each other. In a dead organism, though, the ratio will vary: the unstable isotopes will break down over time, changing the ratio between them. This means that scientists can look at the ratio to figure out an organism's age.
As I mentioned, this form of dating is very accurate and precise. Not only does the sciencr work on its own, it's been confirmed many, many times by dating things of already-known age: when we date something that we know to be from the time of Jesus, for instance, we get an age of 2,000 years.
These same methods tell us that there are examples of homo sapiens that are older than the maximum that carbon dating can date. They also tell us that things like animal pigments used in cave paintings in France are about 40,000 years old.
I suppose you can always find an excuse to disregard this evidence; maybe God made the laws of physics different in the past, maybe it was "angels" who did those paintings and not humans, maybe "deceiving demons" have fooled every nuclear physicist who has ever lived... but those sort of hand-waving dismissals aside, the evidence does point with very high certainty to humanity being at least an order of magnitude older than 9,000 years.
If we werr trying to reconcile a difference of like a century or two, sure: maybe we could appeal to imprecision in dating methods. However, you're claiming that humanity's age is less than a tenth of what reliable dating methods say it is. If those dating methods are that wrong, then all of physics is wrong. This would mean that satellites and nuclear power plants just wouldn't work the way we think they should. I don't know about you, but I get my power from nuclear and my lights still work.