or from the category of rewards for accomplishing a task (juʿālāt), or of partnerships, or of vows and binding undertakings, or of promises and voluntary donations, or is it an independent contract in its own right, standing apart from all of these?

The answer: it is indeed an independent, self-standing contract (1), not included under any of those agreements, for their respective rulings do not apply to it.

The invalidity of classifying it as a lease appears from several angles:

First: it is a revocable contract; either party may annul it before the work begins, unlike a lease.

Second: in a lease the work must be known and within the worker’s ability, whereas in a race the act of coming first is unknown and beyond the competitor’s control—he does not know whether he will win or be outpaced. In a lease this would be pure uncertainty (2).

Third: in leasing, the benefit returns to the lessee and the payment to the worker: one provides money and the other labor, so each profits from what the other offers. In a race, however, the act pertains to the one who comes first.

Fourth: if the hired worker fails to perform, he owes no compensation, whereas the contestant who fails to win forfeits his stake if he was the one who put it up.

Fifth: a lease contract does not require a muḥallil (a third, disinterested participant), whereas on your view this contract does.