Pope and KY wins one and BYU gets the win the following year, or visa versa. Of course the BYU fan in me would want BYU to win both of those matchups, but if BYU were to lose one of those, it wouldn't hurt as bad having it be to Pope in one of those matchups. As you point out, it would be awesome to see a high character LDS guy like Pope take his alma mater and that bluest of blue bloods back to the Promised Land like that.
Other factors about such back to back matchups like that would also be fun: It would be called the "Battle of the Blues" and/or the "Cat Fight", both teams having blue and white as their colors and a cat for a mascot. Or even, dare I say a "Holy War", with both Pope being a person of faith (and his last name to go with that) and of course BYU both being and representing an institution of faith.
Aww heck, why not throw Madsen in there too if he isn't already the coach of BYU at the time?
But mostly, as a BYU fan, I just want to have that experience of seeing BYU finally break through and advance all the way to the Final 4 before I'm dead and it would be even more exciting to see BYU win a game or two there. And such a scenario as above would bring tremendous and positive publicity for the Church in the basketball world, both near and far, hopefully opening some doors and some hearts of some to the Gospel being taught to them. And all the better if your son were to have a roll in and/or otherwise be a part of all that excitement.