I agree with Neon.
It should be his work. The teacher will know what he's done and what you've done anyway. Overzealous parental involvement helps no one and is a waste of time.
2.5 hours doesn't seem unreasonable. What are the resources? If that is an issue, schools can usually help out.
What about them? I disagree with 'also ran' prizes although I absolutely do agree with prizes based on relative achievement. You said that it is based, among other things, on effort.
The problem here isn't his disparaxia. It's his lack of belief in his ability to win. Have you spoken to his teacher?
I'm in education. While I like to think I'd know him well enough by now (over a term into the year) to guess how he may feel about it, a heads up from a parent to let me know he's under pressure and a little disheartened would be helpful.
Get him to complete one of the tasks. Give your teacher a heads up as to how he's feeling and have him submit that one part asap. If your teacher is any good they will glance at it, stop the class and have him show it as such an incredible example of what was wanted.
Those prizes aren't used as a stick to beat other children with and nor are they used purely as a carrot and awarded to the 'best' work. There's usually a good bit of thought into who will benefit most from winning.
If I knew and taught your son, I would consider whether to encourage him throughout the course of the work and then reward him or encourage him, tell him he was second and how, by listening to constructive feedback he was sure to win next time and, of course, he would.
I think you need to work on your sons confidence. Not saying you aren't aware or aren't trying but it should be your focus.
I get the distinct impression on MN (though not in my job) that parents resent being needed for "parental involvement". I hated KS1 and EYFS as well as the demographic at that school, due to the number of parents who washed their hands of their children and wanted teachers to be responsible for everything.
The children who do best at school are the ones with parents who are happy to work with the school but, at the same time, aren't the ones who send their children to bed and do an entire project on their behalf. Some parents are lazy. Some don't understand the purpose of a teacher and school, some are simply a little confused. You don't seem to be one of those 3 OP, but for some reason are against the school giving anything to do outside. Is 2.5 hours a week really that much - yes, on top of spellings (10 mins) and reading (20).