Where the slot goes: Teku, and the counter that called a syncing node healthy
Teku is the only client in this series that answers the question in the title directly. It splits a block's journey into eleven named stages and counts every one of them, so instead of inferring where the slot goes you can read it off: arrival, gossip validation, pre-state retrieval, the engine call, the state transition, the commit.
In the same three days, on the same six machines, Teku's own counters reported that the healthiest node in the fleet was one that had not committed a single block to its canonical chain.
Both of those are worth your attention, and they are the same story. Teku gives you more slot detail than any other client here, and the detail is carried in metric types that will mislead you at least three separate ways if you read them the way their names suggest.

