My DD6(first grade) is in Montessori, and if left to her own devices, she would just read the whole time... So, we pay her COLD HARD CASH, and lots of it for completing her workplan and attending lessons. Each morning, the teacher picks a few jobs and she picks a few, and then she earns wages for work completed. She has become very motivated to complete her plan everyday. I know it's not Montessori philosophy, but it works, and my daughter, who once hated school and thought it was pointless, now loves going to school and earning money. I think she's learning a good work ethic, because in reality we all work for money. As for intrinsic motivation and love of learning, she still has that, but only for 'fun' stuff she can do at home with me, like Beast Academy, etc. We're so lucky that her teacher gives her appropriate work for her ability, which is several grade-levels ahead, but she doesn't like to write and would rather just read, so this system is working for us, and for the most part, she seems to like and benefit from the work she's doing in class, even if she wouldn't do it without the incentive.
