Hate to be a buzzkill here, but after some analysis, I have come to the unhappy conclusion that I would likely do it the same way it is done now. Pretty close to exactly. Including the things I don’t like personally (but understand the reasons).
^^ I think that system, requiring the case of cash, already exists.
Dang it, I am admissions manager at an elite (graduate) school, and no one ever offers me cash. (I am amassing a very nice collection of artwork, but that comes to me when they graduate.)