Ran both tests on the 679.
Shape: skewed, not flat. 324 settle within 6 s of the top of the range (297 s), then a steady tail to about 65 s. KS distance from uniform is 0.495 (the 95% bound for flat is 0.052). The tight 300 s payee shows the same floor without the tail.
Beat: none. Every settlement is its own transaction; 629 blocks hold one and 25 hold two, consistent with its traffic. The commonest gaps are 0–22 s, and only 36 of 678 gaps are multiples of 60 s. Phase concentration within the minute is 0.098 against about 0.04 for random, a slight preference but nowhere near a timer. So it reads as per-request settlement, with that server taking up to about a minute to respond.
Your reconciliation holds: the 23 are all validAfter = 0 and all outside the piles, leaving 8. Four sit 1–3 s under 120 s (a fifth L, four rows), one 5 s under 1800 s, two are batch settlements 29–31 s under 600 s (the 600 pile’s tail), and one at 203 s has no L above it. The 3600 pile is 12 of the 14 boundary rows.
So: five lifetime defaults (60, 120, 300, 600, 3600 s, plus one 1800 s row), one payee whose smear is response time, and one row unexplained.
