Disabling learners moving on to the next section/lesson until they have completed the previous.

Your variables sound all right. Now you need to use them in your triggers:

Jump to subunit 2 when user clicks Next if variable = true. You will need a unique variable to show completion of each subunit.

Of course, none of this matters if you are using a built-in menu. In that case you will need to use a restricted menu. This artilce will help you with that.

https://community.articulate.com/series/articulate-storyline-360/articles/articulate-storyline-360-user-guide-how-to-customize-the-menu#restrict

If you need or prefer to use variables, the sample at this post will show you a way to do it.

https://community.articulate.com/discussions/articulate-storyline/free-sample-restricted-and-free-random-navigation-using-variables-and-triggers 

You will want to use the restricted navigation.