I agree it's an absurd amount of work. I'd even go so far as to say that OP shouldn't have to do it unless they had an extension.

But I don't think that the "should" or "shouldn't" of this situation will matter much to the school, and clearly doesn't matter to the professor. Now, if it was in the syllabus, my advice would be that there's nothing OP can do, and escalating will make things worse and damage their relationship with the people controlling their grades.

Given that it isn't in the syllabus though, I think OP may have way more room to say that it's not reasonable for it to be counted against them. It would still be an uphill battle though.

I don't really like that this is the case, but unfortunately the professor would have to do something incredibly egregious (like, something calling his professional conduct or credentials in question) before most universities would step in.