Might you be able to simulate this with random price development? (I can only do it in Excel, and that way it'd take some time)
If you want to increase the gain via a time-based arbitrage you have to give up some of your longterm price appreciation for the benefit of short-term price fluctuations. It's always difficult to figure out which one is more attractive at certain times. If the price flatlines a reversible rake strategy with a small enough margin will do well. The problem is to be able to predict when the price flatlines and when it starts to rally. If you have too much of a rake involved and you miss the start of a rally, you basically forgo all the opportunity gains coming from that initial slope in the rally.
That said - a reversible rake strategy works best in a scenario where there are huge price inflations and deflations, as you accumulate fiat on the way up and btc on the way down without the need to call the bottoms or the tops. That said - I don't expect bitcoin to depreciate more then 10x anytime soon - other than becoming worthless because of some black swan event.
We know volatility in excess of the frictional trading costs exists. I think this suggests that a slightly more optimal strategy than the SSS must also exist. Like some others have alluded too, it could be an SSS plan (with sells perhaps spaced every decibel, rather then every doubling), but, most importantly where you have a trailing bid at, say, -1.5dB below your last sell point.
Think of it as an SSS plan + a money-pump harvesting the volatility that exists anyways.
I know Risto explained how the trailing bid removes some of your hedge, and I agree. My counter would be that for a given level of retained bitcoin wealth should bitcoin hit $100,000, and an assumed level of volatility, there is a strategy that would produce a higher amount of "raked-USD" than the SSS should bitcoin fail before it gets to $100k+. We just need to find what that strategy is. Ever since I read about Risto's SSS plan, I've wanted to simulate this and some other ideas. But, alas, my real job calls.....