I know this was posted years ago, but I'd like to throw in my two cents, as I can relate to this question. I'm usually in a similar situation: administration not too keen on changes or failing too many students, and sometimes even the other teachers (as I don't work alone) not wanting any extra work in order to grade projects in addition to exams.
I don't think there's a magic solution here, as every group of students is different. But usually they are mostly interested in passing tests by studying as little as possible (and blame this on education systems, that focus on grades and exams instead of students learning at their own pace).
However, you can turn this into something you can use: when you give them a project, you can tell them that it will affect the kind of exam they will be doing. You can even tell them the grade will not only depend on how good or bad they did on those extra activities but will also take into account other stuff, like turning in assignments or completing a phase of a project, presenting to the class (even when it's just showing and explaining the work they did), peer reviewing could also earn them some credit. The better grade they get on the extra activities, the more benefits they will earn. So when it comes to exam time, those that worked the hardest will get the most rewards.
For instance, students that got less than a C in extra activities will have an extra question on their exam (and maybe this question will have a great impact on the overall score, or maybe they will just fail if this question is not correctly answered even if their answers to other questions are correct). Those who got a B will be granted the ability to have a helping sheet (with some information that could help them in the exam -not giving away answers but providng some hints). And finally, those that got an A would have extra points added to their exam.
As I said, every group is different and you might find out this strategy works great one year and not so much the next.