Extrude curve to match another curve

How can I extrude the bottom curve so that it matches the outline of the middle curve

Have you tried lofting the curves?

it ends up doing something like this:

CURVE JOIN.gh (10.4 KB)

Your GH definition only contains three curves, no Loft command.

Using the Loft options, you can choose to align the curves.

CURVE JOIN.gh (16.0 KB)