My understanding is that AS agents are limited to the same tools behind the website... so the website IS the authority. Calling in likely won't open new possibilities, but it can be helpful to get their input.

I played around with EK awards this summer and remember getting MLE-CMB//DXB-LAX to price out. DXB stopover should be no problem. Strangely enough, while asking for stopovers in MLE or CMB, AS.com offered several itineraries involving backtracking through CMB or MLE (ie: CMB-MLE//CMB-MLE-DXB-LAX), so the routing rules musn't be too strict, but I never managed to route through SIN. My goal was to get another A380 segment rather than the regional F. Please let us know if you're successful.

FYI, and it sounds like you've already done this, make sure you search individual segments or at least one-ways without stopovers before taking dates with availability to the multi-city search. Otherwise it's nearly hopeless searching for complicated partner itineraries.