I think I remember hearing hundreds of years for both VSOP and numerical methods. There is too much chaos to trust the results beyond that. Once your semi-major axis has a small amount of error in it, your period has a small amount of error, resulting in error in the placement of the planet on its orbit. This error accumulates orbit after orbit.
Your result isn't completely meaningless, though. You've demonstrated that Uranus transits from Neptune are rare, happening on timescales in the tens of thousands of years.
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