Maybe you are overestimating what the teacher expects for some of the tasks. For a leaflet - I remember in Years 6/7/8 etc producing leaflets over a few lessons, quite details, printed nicely, pictures, research etc, so my immediate response would be to think that was what was needed, and how many hours it would take with a dyspraxic 7 year old. But there's a chance that actually the teacher expects you to do a bit of research together, fold a piece of paper in 3, let him draw bits on each piece, and that's it. It gets them thinking - what should be on the cover? Should I put the title in big letters? What should I draw on the inside then with more details? And that's enough. Objective accomplished.
yes, some children might have parents that will do the whole works with/for them, and a competitive prize doesn't seem ideal if it's only based on final product, but if they do look at effort and so on, then they might be rewarding for all sorts of other things, not just the ones with parent-perfect presentation.
Given that it is something you have to do, and prizes are involved, you could try to change his view (and possibly yours) about the three prizes being the only thing that matters - "all that effort, and only three get rewarded" - by reminding him that the point of it is to learn about the topic, to have fun making stuff instead of just writing it or doing a test, to be able to show the teacher and other children what they've learned, to be rewarded by the teacher giving him positive feedback about it, other children liking the cooking samples, or whatever they get to do. We used to do science/history fair projects once a year that sounded a bit like this, and while there were prizes, the big thing was the day where we brought them in, looking at each others projects, seeing how they'd done things, trying out samples or activities or watching things they'd made/models/films. Some of them did have loads of parent help, and probably wasn't fair to judge on that, but even still, there was such a variety and we all thought different ones were the best. Perhaps you could keep trying to encourage him to think of ways that it might be rewarding that don't mean having to win a prize.