I have no solution to offer, but I'd just like to say I've had a almost identical scenario but with another airline. (which kind of indicates this issue lies with A3)

What can be established by contacting the operating airline (SQ in this case) is to find out it they have the traveller on record. When A3 say "retro claim failed because traveller was not onboard that flight" it is good to know operating airline told you everything is OK on their side. You can then with confidence ask them to re-try the claim. Only an agent at A3 can re-try a claim and before they do, make sure every thing in the claim is exactly the same as the details the operator has.

And as said above, operating airlines are unlikely to be very helpful in these cases.