but asking for a heading of 310 was inexcusable.
Actually - why ? OK, from SIN it should be pretty obvious which way to go, even 'just' with coordinates, but if ATC ask you to fly to an unfamiliar waypoint w/o giving you a heading, I guess this could indeed happen, as the WP may be to the North. I've had things like that happen (and no, I don't fly any heavy metal), when ATC in unfamiliar airspace asked me to fly to some WP I couldn't immediately locate on the chart.
Actually another pro-GPS argument as it vastly improves your situational awareness,
if you know how to use it. To me, this is the crux: know the equipment in your a/c.