Switching to static front page

Does anyone have advice regarding how you can switch to a static WordPress front page and yet still have a quarter of the page dedicated to showing titles of latest posts?

Yes, you could create a custom home / front page template > select that template for your main page and you could code it exactly to your requirements.

Say you create a page > Home then in Settings > Reading > Select a static page > here you can select the page you want.
When you create the Home page it will ask you whether you want default template or you can select a custom template. Now the custom template you can code with say half page static and the remaining half page with latest posts etc as per your requirement.