I went to Singapore this past July and, like you, strongly prefer OW carriers - but I got a fare of $1246 on NW (could have been $1046, but that's another tale) while OW's best was $3000+. Much as I hate to put miles in the "wrong" place, with that price difference I can do mileage runs to make up the loss and still come out ahead.

The moral: unless this trip is your last shot at making EXP or whatever, or you want to use an upgrade coupon that you'd have to discard otherwise, don't restrict yourself ahead of time. This may be heresy to some dedicated mileage hounds, but there is such as thing as spending more for miles than they could ever be worth. It may make sense to compromise your airline principles for the savings.