It’s a noble goal to change the incentives, but how will you prevent the headlines from this event being “students prove Collatz conjecture with Claude” and instead be “students give great explanation of Collatz conjecture proof”?
I suspect you will find there is less appetite at the funding level for this kind of thing though, because what your funders really care about is generating headlines in front of their IPOs, and this kind of thing wouldn't generate the same headlines. I would be pleasantly surprised to be proved wrong of course.
EDIT: A more cynical point that I should add - I also suspect your funders would have less appetite for this kind of marathon because LLMs don't seem to be very good at this yet, which kind of points to the whole problem: so far, LLMs seem good at producing Lean proofs but not very good at the rest, but that fact is being lost in the media narrative, and "the rest" is actually the part that matters.