[EricH]

Originally Posted by Kevin Leonard

What if (bold idea), before week 7, FIRST polls a number of experts on who the best 20 or so teams to not make championships are (kind of like this, but two weeks earlier) and invites them to the championship event.

That, I think, would be one of the best ideas. Let's expand towards original intent of the question.

1) FIRST polls experts on best 50 teams to not CURRENTLY make championships. (Trust me, there's a reason this number is so high.) This happens sometime around Week 6.
2) FIRST looks at who still has a chance to qualify (playing Week 7, maybe playing Week 6), or is near the top of the waitlist. These teams are set aside.
3) FIRST looks at geography and representation. Teams from underrepresented areas get higher priority than teams that are from fully represented areas.
4) The combined "best teams" and "underrepresented areas' teams" sorts determine the order of offering--but only to the top 25 on the combined list.
5) After Week 7 plays, the list is revisited. The bottom 25 and the teams that were set aside are now eligible for invites.