If I may, the reason airlines have a minimum stay is to separate the more flexible (and more expensive) economy tickets from the lowest available Y seat. No airline is going to make money flying pax to SIN for USD 259.00 roundtrip with no minimun stay. They want you to be forced into buying the pricier Y fares. Sometimes a deal comes along as just returned from a LAX-SIN MR that was offered at the rate I've mentioned with no minimum stay rules. The fare lasted only a few days before NW changed the fare rules, not the price, to require a 6 day minimum stay.

As it usually happens, cost vs. convenience at their usual places at opposite ends of the teeter-totter, just where airlines like it. Unless you can sacrafice convenience, don't expect cost to be low.