Also notice how there's a small gap in the Faucet withdrawals whenever a block is generated. This probably tells us something about network propagation speed or somesuch.
No. After a new block, the faucet pays out from its ~45 BTC transaction, then pays out from a smaller transaction until the next block. The gap will disappear when the faucet funds drop below 45 BTC, when there's only one transaction available to pay out from.