By my own counting from the
ranking page, there are 4 Chairman's award winning teams outside the top 60 in points (and I'll assume the Hartford winner will be too, for more conservative math). So that means the cutoff right now (assuming every team goes) is at team ranking #55, which has 67 points.
However, there's still other awards, so any team with at least 62 points (rank 71) could swing up, unless teams win multiple awards. It's probably safe to assume that every team with at least 66+5 = 71 points is in, although EI and RAS could swing this a little more.