If you go to the individual solutions, the text description tells you if it's stable. There's also a slider that allows you to perturb the orbit so you can see for yourself when you perturb it.
I'm curious why you think a disclaimer about the accuracy of predicting the future is irrelevant to a timeline of predictions about the far future. Indeterminacy and free will can absolutely affect most of the predictions listed on this timeline.
Indeed at the bottom tfb quotes heights of 190-250km for model calculations.
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