How do I rescale artwork to fit the artboard?

Why not Fit Artboard to your Artwork? Object->Artboards>Fit to Selected Art.

select all

window >> transform

Enable scel stroke & effects if needed

To keep proportion: enter either the width or the height (your choice)

To distort to artboard size : click the chain to so that width adn height are not constrained, enter both dimensions

For X & Y enter 0 in both

The white artboard has different proportions. You will also need to rearrange that illustration.