Is there a better way to perform a double split operation?

Not in my book. I know different ways, but if I were to use a double split, I'd do it more or less in the same way.

Is there a better way to extract the date from the table?

If it's just to retrieve the first sequence of non-space characters after the penultimate newline, you could also write:

my ($date) = /(\S+)[^\n]*$/;
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But that doesn't mean it's faster. Or clearer.