You are right - btcmine was the most difficult of the pools to scrape, because it does not indicate actual rewards on a per-round basis. The rounds are "earned" some time after they are "confirmed"! I've cleaned up the stats a bit (a couple of the rounds were mis-attributed), see if these are any better. However, there will always be rounds with very low or even zero rewards in score-based pools, because they have very high variability. Imagine: due to the exponential decay, all the shares that are worth 1.0 BTC now, will be worth only 0.00000615 BTC one hour from now - 12 decay periods later. And rounds can last for many hours...

Again, the score-based rewards result in higher variability. The expected utility is still above 100% for most rounds. However, since the expected utility of score-based pools levels out at about 90% during long rounds, they are usually the fallback option when all the other pools are also having long rounds (and shares-based expected utility keeps dropping to zero). If this happens too often, I might even have to add a solo pool option and generate my own getworks for the miners during dry periods! Being the go-to fallback option, score-based pools are usually not as profitable overall (but still more profitable than their operators would like you to think). It will take more time though to see whether the actual average rewards will match my utility predictions.

It is integral to maximize the number of pools in rotation. At many timepoints, even those with fees have higher expected utility than any other pool. If pools implement fair algorithms that make the expected utility constant throughout time, then fees will indeed play a greater role.