Montessori, or Jenaplan (a Dutch/German thing, which was the one I went to).
There was a bit of 'prison' in that there was a certain number of fixed tasks to complete each week in areas such as Math, Dutch and English. But one could pick which, and mostly even check them oneself. Once done, the rest of the time was free to work on projects and things just like you described above (the carrot :-). Often by Wednesday afternoon I was done.
It thus worked wonderfully for me, though it may not be for everyone. But when I have kids they are definitely going to a Jenaplan-type school. As it never felt like a prison to me and instilled a love of learning, and ability to plan and reward myself (besides other positive things such as a sense of equality towards others, including bosses & profs)
School != School. Shop around before you reinvent.