Membership Name-Your-Own Price (above Minimum) on Contribution Page
I gather you are not looking for a development solution (ie. extension, custom template, etc.) since the API/template system is extremely extensible.

If that is the case you might consider creating a button or link on the form (if you are slick you might adjust the css or use jquery to place it in the price-set.) that takes the user to a separate contribution page with the name your own price. 

I realize it does not match the mockup but it may serve the functional requirements.