detailed analysis.

Several things make what you propose near impossible.

First, no way will BYU ever surrender the responsibility of hiring and firing coaches to a group of donors, no matter how large and wealthy. How recently did they finally allow a building on campus to be named after someone other than a GA or well-known historical LDS figure? How long did it take the basketball MCA to come to fruition and why? Look at the Coaches Circle that currently raises funds to pay and retain coaches. It is part of the Cougar Club which is controlled by the university. This will not change.
http://cougarclub.com/coaches-circle

Second, we need to get into a P5 conference to get to a next level of revenue generation, visibility, and sustainability. Any coach that comes in, no matter how glitzy, will have to confront life as one of the last remaining independents and all the challenges it brings.

Third, we would need to improve recruiting or you'll never achieve better results. Without P5 status, as acougfan stated, it will not substantially improve. A new head coach will have the constraint of independence, the honor code, and the academic standards to uphold and accept.

And yes, even if you clear all of these hurdles, you are guaranteed nothing. Here is a list of 11, most from very big and prestigious programs, and it doesn't even include Sarkisian, Richt, and Kiffin. What a double waste of money, first to bring them in, and next to have unsatisfactory results only to keep paying them for their poor performance for years after. and several of these are at schools with lots of practice at doing this, with much more resources than BYU has.
http://espn.go.com/college-football/story/_/id/12963172/notre-dame-auburn-nebraska-pay-fired-coaches-huge-buyouts

Got an extra few million $ to burn?