This sounds like a great idea you are cooking up and the question you raise is fascinating. So let me give you one man's ideas to throw into the mix.
As far as threshold criteria go, I'm not sure you need an age/rank/years of service limit beyond the age 14 requirement Phimont imposes. After all, a new Venturer could go to Philmont in the first year with no traditional scout ranks or time in a troop.
From other experiences, I would suggest that your application require:
(1) An essay from the youth on "Why I want to go to Philmont."
(2)A recommendation/nomination from the youth's Scoutmaster/Crew Advisor. (This will also help you weed out the not-really-needy and not-really-committed ones.)
(3) An essay from a parent/caregiver on "Why I want my kid to go to Philmont and how I'll support him."
These kinds of things start to get some skin in the game without actual dollars involved.
You mentioned the idea of starting with 20 and weeding it down to 10 as you prepare for Philmont. This idea bothers me, probably because it reminds me of reality television and. I also think it will be hard to do this in a way that is consistent with Scouting values. With that said, I suggest you start with the maximum number of youth allowed by Philmont with maybe two alternates, who are identified before the shakedown process. To be gracious, you might commit to giving a campership to a good council summer camp to any alternate that doesn't make the crew.
As far as the economic skin in the game question goes, I'd suggest some variation on the Habitat for Humanity model, where the youth has to put in sweat equity in order to go. If you wanted to, you could make the amount of the campership dependent on cheerful participation in the shakedown activities. A youth that does everything needed to prepare gets a full ride while a youth that misses opportunities has to put up more of his own money.
I assume you've already thought of this, but some of your campership money or effort will need to go into buying/borrowing gear for the youth.
Best of luck to you,