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I like Mark M's solution best. The double-ended continuous sheet led to both corners has some problems already mentioned: keeping the ends more or less the same length requires a bit of attention to which one you last adjusted and how much, and the extra line and turns are not needed and add resistance when letting out the sail in light air. JimB mentioned the possibility of tangling the sheet around the engine, but I don't think that's likely. It stays in front of the gallows, so there's good separation. The tiller is in more danger of being snagged.
The companionway traveler also has some problems. It's in the way, can chomp fingers, is often across a passenger from the helmsman, and most important to me, it gets in the way of having a larger Bimini top. The last problem is somewhat shared by the current factory arrangement - the upwind part of the double ended sheet is draped across the Bimini when off the wind.
Mark's answer solves all the problems with both setups best, IMO. It has only one end, doesn't have any unnecessary mechanical advantage, has less overall length and is more likely to stay clear of the engine and the tiller, is out of the way of passengers, is near the helmsman, and will run to the side of a Bimini when off the wind. Way to go, Mark!
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